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<title>Library Evolutionary Algorithms for Clustering (LEAC): um Namespace Reference</title>
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<p>Unsupervised measures for clustering analysis.  
<a href="#details">More...</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a62470812baa18b85111f619b35a012c8"><td class="memTemplParams" colspan="2">template&lt;typename T_FEATURE , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a62470812baa18b85111f619b35a012c8"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a62470812baa18b85111f619b35a012c8">maxDistCjCjp</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:a62470812baa18b85111f619b35a012c8"><td class="mdescLeft">&#160;</td><td class="mdescRight">Find the maximum distance beteen the centroids.  <a href="#a62470812baa18b85111f619b35a012c8">More...</a><br /></td></tr>
<tr class="separator:a62470812baa18b85111f619b35a012c8"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3b1be7542cfeaffb6040f73e0e3c8054"><td class="memTemplParams" colspan="2">template&lt;typename T_FEATURE , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a3b1be7542cfeaffb6040f73e0e3c8054"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a3b1be7542cfeaffb6040f73e0e3c8054">minDistCjCjp</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="separator:a3b1be7542cfeaffb6040f73e0e3c8054"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae2f7f8496b7cfe11e8411fe1102bcf22"><td class="memTemplParams" colspan="2">template&lt;typename T_CLUSTERIDX , typename T_FEATURE , typename T_METRIC &gt; </td></tr>
<tr class="memitem:ae2f7f8496b7cfe11e8411fe1102bcf22"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#ae2f7f8496b7cfe11e8411fe1102bcf22">minDistCjCjp</a> (const T_CLUSTERIDX aicidx_Clusterj, const <a class="el" href="classmat_1_1_matrix_base.html">mat::MatrixBase</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="separator:ae2f7f8496b7cfe11e8411fe1102bcf22"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1aab06d6281016beb6769fea5032ddb9"><td class="memTemplParams" colspan="2">template&lt;typename T_FEATURE , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a1aab06d6281016beb6769fea5032ddb9"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a1aab06d6281016beb6769fea5032ddb9">sumMinCjCjp</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:a1aab06d6281016beb6769fea5032ddb9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculate minimum sum of distances between all centroids.  <a href="#a1aab06d6281016beb6769fea5032ddb9">More...</a><br /></td></tr>
<tr class="separator:a1aab06d6281016beb6769fea5032ddb9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a92550dabf7b2bbc875e88e4b41850531"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a92550dabf7b2bbc875e88e4b41850531"><td class="memTemplItemLeft" align="right" valign="top">std::vector&lt; T_METRIC &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a92550dabf7b2bbc875e88e4b41850531">avgRadiusClusterK</a> (const <a class="el" href="classmat_1_1_matrix_base.html">mat::MatrixBase</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clusters, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="separator:a92550dabf7b2bbc875e88e4b41850531"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4667b7aa0e2926c0f0f94afaa4a0dcf2"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a4667b7aa0e2926c0f0f94afaa4a0dcf2"><td class="memTemplItemLeft" align="right" valign="top">std::vector&lt; T_METRIC &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a4667b7aa0e2926c0f0f94afaa4a0dcf2">maxRadiusClusterK</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clusters, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:a4667b7aa0e2926c0f0f94afaa4a0dcf2"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculates the maximum radius of a cluster for a partition.  <a href="#a4667b7aa0e2926c0f0f94afaa4a0dcf2">More...</a><br /></td></tr>
<tr class="separator:a4667b7aa0e2926c0f0f94afaa4a0dcf2"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ac9c4b9777bb97ada898b3d1bc2621996"><td class="memTemplParams" colspan="2">template&lt;typename T_CLUSTERIDX , typename INPUT_ITERATOR , typename T_FEATURE , typename T_METRIC &gt; </td></tr>
<tr class="memitem:ac9c4b9777bb97ada898b3d1bc2621996"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#ac9c4b9777bb97ada898b3d1bc2621996">diameterClusterKj</a> (const T_CLUSTERIDX aicidx_Clusterj, const <a class="el" href="classds_1_1_partition_linked.html">ds::PartitionLinked</a>&lt; T_CLUSTERIDX &gt; &amp;aipartlink_memberShip, INPUT_ITERATOR aiiterator_instfirst, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="separator:ac9c4b9777bb97ada898b3d1bc2621996"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:acbada65717c92ac0a22d2f71c61526d1"><td class="memTemplParams" colspan="2">template&lt;typename T_CLUSTERIDX , typename INPUT_ITERATOR , typename T_FEATURE , typename T_METRIC &gt; </td></tr>
<tr class="memitem:acbada65717c92ac0a22d2f71c61526d1"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#acbada65717c92ac0a22d2f71c61526d1">radiusClusterKj</a> (const T_CLUSTERIDX aicidx_Clusterj, const T_FEATURE *ait_centroid, const <a class="el" href="classds_1_1_partition_linked.html">ds::PartitionLinked</a>&lt; T_CLUSTERIDX &gt; &amp;aipartlink_memberShip, INPUT_ITERATOR aiiterator_instfirst, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:acbada65717c92ac0a22d2f71c61526d1"><td class="mdescLeft">&#160;</td><td class="mdescRight">Radius of Clusterj.  <a href="#acbada65717c92ac0a22d2f71c61526d1">More...</a><br /></td></tr>
<tr class="separator:acbada65717c92ac0a22d2f71c61526d1"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a659ac7560d0d7b1243dd9ef479e2f80f"><td class="memTemplParams" colspan="2">template&lt;typename T_METRIC , typename T_FEATURE , typename T_CLUSTERIDX , typename INPUT_ITERATOR &gt; </td></tr>
<tr class="memitem:a659ac7560d0d7b1243dd9ef479e2f80f"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a659ac7560d0d7b1243dd9ef479e2f80f">D2</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixrowt_S, const <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clustersBkinCi, const <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clustersBi, const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixrowt_Vi, const std::vector&lt; T_METRIC &gt; &amp;aivectorr_meanRadiusBk, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="separator:a659ac7560d0d7b1243dd9ef479e2f80f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:afd59ddda70e29cf009ccb0113bf0d668"><td class="memTemplParams" colspan="2">template&lt;typename T_FEATURE , typename T_INSTANCES_CLUSTER_K , typename T_CLUSTERIDX , typename T_METRIC &gt; </td></tr>
<tr class="memitem:afd59ddda70e29cf009ccb0113bf0d668"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#afd59ddda70e29cf009ccb0113bf0d668">Dintra</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixrowt_S, const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixrowt_Vi, const std::vector&lt; T_INSTANCES_CLUSTER_K &gt; &amp;aivectort_numInstBi, const <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clustersBkinCi, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:afd59ddda70e29cf009ccb0113bf0d668"><td class="mdescLeft">&#160;</td><td class="mdescRight">Dintra <a class="el" href="citelist.html#CITEREF_Tseng:Yang:GAclusteringVarK:CLUSTERING:2001">[38]</a>.  <a href="#afd59ddda70e29cf009ccb0113bf0d668">More...</a><br /></td></tr>
<tr class="separator:afd59ddda70e29cf009ccb0113bf0d668"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae447a0558845df2a5f208de33081c167"><td class="memTemplParams" colspan="2">template&lt;typename T_FEATURE , typename T_INSTANCES_CLUSTER_K , typename T_CLUSTERIDX , typename T_METRIC &gt; </td></tr>
<tr class="memitem:ae447a0558845df2a5f208de33081c167"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#ae447a0558845df2a5f208de33081c167">Dinter</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixrowt_S, const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixrowt_Vi, const std::vector&lt; T_INSTANCES_CLUSTER_K &gt; &amp;aivectort_numInstBi, const <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clustersBkinCi, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:ae447a0558845df2a5f208de33081c167"><td class="mdescLeft">&#160;</td><td class="mdescRight">Dinter <a class="el" href="citelist.html#CITEREF_Tseng:Yang:GAclusteringVarK:CLUSTERING:2001">[38]</a>.  <a href="#ae447a0558845df2a5f208de33081c167">More...</a><br /></td></tr>
<tr class="separator:ae447a0558845df2a5f208de33081c167"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a826858480b2fb93f9bd133725866b3d9"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a826858480b2fb93f9bd133725866b3d9"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a826858480b2fb93f9bd133725866b3d9">e1</a> (const T_FEATURE *aiarrayt_meanInstances, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:a826858480b2fb93f9bd133725866b3d9"><td class="mdescLeft">&#160;</td><td class="mdescRight">e1 <a class="el" href="citelist.html#CITEREF_Maulik:Bandyopadhyay:GAclustering:IndexI:2002">[33]</a>  <a href="#a826858480b2fb93f9bd133725866b3d9">More...</a><br /></td></tr>
<tr class="separator:a826858480b2fb93f9bd133725866b3d9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a2c9cfebda53391da144943d8092d3dd6"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename FUNCINSTFREQUENCY , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a2c9cfebda53391da144943d8092d3dd6"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a2c9cfebda53391da144943d8092d3dd6">e1</a> (const T_FEATURE *aiarrayt_meanInstances, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist, const FUNCINSTFREQUENCY func_instfrequency)</td></tr>
<tr class="memdesc:a2c9cfebda53391da144943d8092d3dd6"><td class="mdescLeft">&#160;</td><td class="mdescRight">e1 <a class="el" href="citelist.html#CITEREF_Maulik:Bandyopadhyay:GAclustering:IndexI:2002">[33]</a> for frequent instances  <a href="#a2c9cfebda53391da144943d8092d3dd6">More...</a><br /></td></tr>
<tr class="separator:a2c9cfebda53391da144943d8092d3dd6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aaccb7dacc3cb2d8cd7349517387c6dfb"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </td></tr>
<tr class="memitem:aaccb7dacc3cb2d8cd7349517387c6dfb"><td class="memTemplItemLeft" align="right" valign="top">std::tuple&lt; std::vector&lt; T_METRIC &gt;, std::vector&lt; <a class="el" href="common_8hpp.html#a3f6c33fb604556cdc425e7aa2289d009">uintidx</a> &gt; &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#aaccb7dacc3cb2d8cd7349517387c6dfb">sumDistInstCentInK</a> (const <a class="el" href="classmat_1_1_matrix_base.html">mat::MatrixBase</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clusters, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:aaccb7dacc3cb2d8cd7349517387c6dfb"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes the overall between-cluster variance <img class="formulaInl" alt="$SS_B$" src="form_65.png"/> and the number of instances in each cluster.  <a href="#aaccb7dacc3cb2d8cd7349517387c6dfb">More...</a><br /></td></tr>
<tr class="separator:aaccb7dacc3cb2d8cd7349517387c6dfb"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a5d6878cc3f6d19cbe897b143e94398fa"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename FUNCINSTFREQUENCY , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a5d6878cc3f6d19cbe897b143e94398fa"><td class="memTemplItemLeft" align="right" valign="top">std::vector&lt; T_METRIC &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a5d6878cc3f6d19cbe897b143e94398fa">sumDistInstCentInK</a> (const <a class="el" href="classmat_1_1_matrix_base.html">mat::MatrixBase</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clusters, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist, const FUNCINSTFREQUENCY func_instfrequency)</td></tr>
<tr class="memdesc:a5d6878cc3f6d19cbe897b143e94398fa"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes the overall between-cluster variance <img class="formulaInl" alt="$SS_B$" src="form_65.png"/> for instances for frequent instances.  <a href="#a5d6878cc3f6d19cbe897b143e94398fa">More...</a><br /></td></tr>
<tr class="separator:a5d6878cc3f6d19cbe897b143e94398fa"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3d80a7d08b3df236552d73f457543a36"><td class="memTemplParams" colspan="2">template&lt;typename T_FEATURE , typename T_INSTANCES_CLUSTER_K , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a3d80a7d08b3df236552d73f457543a36"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a3d80a7d08b3df236552d73f457543a36">ssb</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, const T_FEATURE *aiarrayt_meanInstances, const std::vector&lt; T_INSTANCES_CLUSTER_K &gt; &amp;aivectort_numInstancesClusterK, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:a3d80a7d08b3df236552d73f457543a36"><td class="mdescLeft">&#160;</td><td class="mdescRight">The overall between-cluster variance ssb.  <a href="#a3d80a7d08b3df236552d73f457543a36">More...</a><br /></td></tr>
<tr class="separator:a3d80a7d08b3df236552d73f457543a36"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a68fe0b2b154800cd10afb48bb8b33eb1"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_INSTANCES_CLUSTER_K , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a68fe0b2b154800cd10afb48bb8b33eb1"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a68fe0b2b154800cd10afb48bb8b33eb1">ssbreeval</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, const std::vector&lt; T_INSTANCES_CLUSTER_K &gt; &amp;aivectort_numInstancesClusterK, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="separator:a68fe0b2b154800cd10afb48bb8b33eb1"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a02c5655fb5595af79e18a1462114be29"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a02c5655fb5595af79e18a1462114be29"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a02c5655fb5595af79e18a1462114be29">VRC</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clusters, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_squaredDist)</td></tr>
<tr class="separator:a02c5655fb5595af79e18a1462114be29"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a6336207d868d7879d55dd09259b4fab6"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a6336207d868d7879d55dd09259b4fab6"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a6336207d868d7879d55dd09259b4fab6">VRCreeval</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clusters, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_squaredDist)</td></tr>
<tr class="separator:a6336207d868d7879d55dd09259b4fab6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a87db67beee15dca61595892f84a94315"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a87db67beee15dca61595892f84a94315"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a87db67beee15dca61595892f84a94315">WBIndex</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clusters, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_squaredDist)</td></tr>
<tr class="separator:a87db67beee15dca61595892f84a94315"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aaa61fb14db29fe31548da280b92eb35f"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </td></tr>
<tr class="memitem:aaa61fb14db29fe31548da280b92eb35f"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#aaa61fb14db29fe31548da280b92eb35f">WBIndexreeval</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clusters, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_squaredDist)</td></tr>
<tr class="separator:aaa61fb14db29fe31548da280b92eb35f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a2dbfacd88668ea38547ceb1521d758b0"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a2dbfacd88668ea38547ceb1521d758b0"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a2dbfacd88668ea38547ceb1521d758b0">scoreFunction</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clusters, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:a2dbfacd88668ea38547ceb1521d758b0"><td class="mdescLeft">&#160;</td><td class="mdescRight">Score function ( <img class="formulaInl" alt="$SF$" src="form_75.png"/>) <a class="el" href="citelist.html#CITEREF_Sandro:Benny:IanF:ClusteringMeasure:2007">[36]</a>.  <a href="#a2dbfacd88668ea38547ceb1521d758b0">More...</a><br /></td></tr>
<tr class="separator:a2dbfacd88668ea38547ceb1521d758b0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a31ab0871217029a7b79267bd81735914"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a31ab0871217029a7b79267bd81735914"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a31ab0871217029a7b79267bd81735914">scoreFunctionreeval</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clusters, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="separator:a31ab0871217029a7b79267bd81735914"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a00ec8c8958c649a61b3094ffe6547b10"><td class="memTemplParams" colspan="2">template&lt;typename T_CLUSTERIDX , typename INPUT_ITERATOR , typename T_FEATURE , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a00ec8c8958c649a61b3094ffe6547b10"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a00ec8c8958c649a61b3094ffe6547b10">distMinIntraClusterKj</a> (const T_CLUSTERIDX aicidx_Clusterj, const <a class="el" href="classds_1_1_partition_linked.html">ds::PartitionLinked</a>&lt; T_CLUSTERIDX &gt; &amp;aipartlink_memberShip, INPUT_ITERATOR aiiterator_instfirst, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:a00ec8c8958c649a61b3094ffe6547b10"><td class="mdescLeft">&#160;</td><td class="mdescRight">Distance min intra cluster.  <a href="#a00ec8c8958c649a61b3094ffe6547b10">More...</a><br /></td></tr>
<tr class="separator:a00ec8c8958c649a61b3094ffe6547b10"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a5079e5e39be0feefeda22a8033fd28be"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_CLUSTERIDX , typename T_FEATURE , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a5079e5e39be0feefeda22a8033fd28be"><td class="memTemplItemLeft" align="right" valign="top">std::vector&lt; T_METRIC &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a5079e5e39be0feefeda22a8033fd28be">diameterClusterK</a> (INPUT_ITERATOR aiiterator_instfirst, const <a class="el" href="classds_1_1_partition_linked.html">ds::PartitionLinked</a>&lt; T_CLUSTERIDX &gt; &amp;aipartlink_memberShip, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="separator:a5079e5e39be0feefeda22a8033fd28be"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa66fd9714651a71aaa33964fa0ab7012"><td class="memTemplParams" colspan="2">template&lt;typename T_CLUSTERIDX , typename T_METRIC &gt; </td></tr>
<tr class="memitem:aa66fd9714651a71aaa33964fa0ab7012"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#aa66fd9714651a71aaa33964fa0ab7012">DunnIndex</a> (<a class="el" href="classmat_1_1_matrix_triang.html">mat::MatrixTriang</a>&lt; T_METRIC &gt; &amp;aimatrixtriagt_dissimilarity, <a class="el" href="classds_1_1_partition_linked.html">ds::PartitionLinked</a>&lt; T_CLUSTERIDX &gt; &amp;aipartlink_memberShip)</td></tr>
<tr class="memdesc:aa66fd9714651a71aaa33964fa0ab7012"><td class="mdescLeft">&#160;</td><td class="mdescRight">The Dunn Index (DI) <a class="el" href="citelist.html#CITEREF_Dunn:ClusterMeasure:CS:1974">[15]</a> <a class="el" href="citelist.html#CITEREF_Zhang:Cao:KernelclusteringLabelKVar:2011">[39]</a>.  <a href="#aa66fd9714651a71aaa33964fa0ab7012">More...</a><br /></td></tr>
<tr class="separator:aa66fd9714651a71aaa33964fa0ab7012"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a46e5d5dc027dab5f0374eb25cd8d4168"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a46e5d5dc027dab5f0374eb25cd8d4168"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a46e5d5dc027dab5f0374eb25cd8d4168">DunnIndex</a> (INPUT_ITERATOR aiiterator_instfirst, const <a class="el" href="classds_1_1_partition_linked.html">ds::PartitionLinked</a>&lt; T_CLUSTERIDX &gt; &amp;aipartlink_memberShip, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:a46e5d5dc027dab5f0374eb25cd8d4168"><td class="mdescLeft">&#160;</td><td class="mdescRight">The Dunn Index (DI) <a class="el" href="citelist.html#CITEREF_Dunn:ClusterMeasure:CS:1974">[15]</a> <a class="el" href="citelist.html#CITEREF_Zhang:Cao:KernelclusteringLabelKVar:2011">[39]</a>.  <a href="#a46e5d5dc027dab5f0374eb25cd8d4168">More...</a><br /></td></tr>
<tr class="separator:a46e5d5dc027dab5f0374eb25cd8d4168"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aaf89404618e7aef4f4bd8398118c70b8"><td class="memTemplParams" colspan="2">template&lt;typename T_FEATURE , typename INPUT_ITERATOR , typename T_CLUSTERIDX , typename T_METRIC &gt; </td></tr>
<tr class="memitem:aaf89404618e7aef4f4bd8398118c70b8"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#aaf89404618e7aef4f4bd8398118c70b8">simplifiedDunnIndex</a> (const <a class="el" href="classmat_1_1_matrix_base.html">mat::MatrixBase</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const <a class="el" href="classds_1_1_partition_linked.html">ds::PartitionLinked</a>&lt; T_CLUSTERIDX &gt; &amp;aipartlink_memberShip, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:aaf89404618e7aef4f4bd8398118c70b8"><td class="mdescLeft">&#160;</td><td class="mdescRight">The Simplified Dunn Index (SDI)  <a href="#aaf89404618e7aef4f4bd8398118c70b8">More...</a><br /></td></tr>
<tr class="separator:aaf89404618e7aef4f4bd8398118c70b8"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a46870f8491e49e0e08ceb0e2f5434bb1"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_INSTANCES_CLUSTER_K , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a46870f8491e49e0e08ceb0e2f5434bb1"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a46870f8491e49e0e08ceb0e2f5434bb1">CSmeasure</a> (INPUT_ITERATOR aiiterator_instfirst, const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, const <a class="el" href="classds_1_1_partition_linked_num_inst.html">ds::PartitionLinkedNumInst</a>&lt; T_CLUSTERIDX, T_INSTANCES_CLUSTER_K &gt; &amp;aipartlinknuminst_memberShip, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:a46870f8491e49e0e08ceb0e2f5434bb1"><td class="mdescLeft">&#160;</td><td class="mdescRight">CS measure <a class="el" href="citelist.html#CITEREF_Chou:Su:Lai:ClusterMeasure:CS:2004">[12]</a> <a class="el" href="citelist.html#CITEREF_Das:Abraham:Konar:GAclusteringLabelKVar:ACDE:2008">[13]</a>.  <a href="#a46870f8491e49e0e08ceb0e2f5434bb1">More...</a><br /></td></tr>
<tr class="separator:a46870f8491e49e0e08ceb0e2f5434bb1"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a5cd2a0a7fb84c32e07af00e249d880d2"><td class="memTemplParams" colspan="2">template&lt;typename T_CLUSTERIDX , typename T_INSTANCES_CLUSTER_K , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a5cd2a0a7fb84c32e07af00e249d880d2"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a5cd2a0a7fb84c32e07af00e249d880d2">silhouette</a> (<a class="el" href="classmat_1_1_matrix_triang.html">mat::MatrixTriang</a>&lt; T_METRIC &gt; &amp;aimatrixtriagt_dissimilarity, <a class="el" href="classds_1_1_partition_linked_num_inst.html">ds::PartitionLinkedNumInst</a>&lt; T_CLUSTERIDX, T_INSTANCES_CLUSTER_K &gt; &amp;aipartlinknuminst_memberShip)</td></tr>
<tr class="memdesc:a5cd2a0a7fb84c32e07af00e249d880d2"><td class="mdescLeft">&#160;</td><td class="mdescRight">Silhouette <a class="el" href="citelist.html#CITEREF_Alves:etal:GAclusteringLabelKVar:FEAC:2006">[2]</a>.  <a href="#a5cd2a0a7fb84c32e07af00e249d880d2">More...</a><br /></td></tr>
<tr class="separator:a5cd2a0a7fb84c32e07af00e249d880d2"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:abfb804a3adf4382c6b4efe519f2ce6cb"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_CLUSTERIDX , typename T_INSTANCES_CLUSTER_K , typename T_METRIC , typename T_FEATURE &gt; </td></tr>
<tr class="memitem:abfb804a3adf4382c6b4efe519f2ce6cb"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#abfb804a3adf4382c6b4efe519f2ce6cb">silhouette</a> (INPUT_ITERATOR aiiterator_instfirst, <a class="el" href="classds_1_1_partition_linked_num_inst.html">ds::PartitionLinkedNumInst</a>&lt; T_CLUSTERIDX, T_INSTANCES_CLUSTER_K &gt; &amp;aipartlinknuminst_memberShip, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:abfb804a3adf4382c6b4efe519f2ce6cb"><td class="mdescLeft">&#160;</td><td class="mdescRight">Silhouette <a class="el" href="citelist.html#CITEREF_Kaufman:Rousseeuw:Book:ClusterAnalysis:1990">[25]</a>.  <a href="#abfb804a3adf4382c6b4efe519f2ce6cb">More...</a><br /></td></tr>
<tr class="separator:abfb804a3adf4382c6b4efe519f2ce6cb"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0be96553f39d25c65bfea9c45f05eaae"><td class="memTemplParams" colspan="2">template&lt;typename T_CLUSTERIDX , typename T_INSTANCES_CLUSTER_K , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a0be96553f39d25c65bfea9c45f05eaae"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a0be96553f39d25c65bfea9c45f05eaae">silhouette</a> (const <a class="el" href="common_8hpp.html#a3f6c33fb604556cdc425e7aa2289d009">uintidx</a> aiui_idxInstance, const T_CLUSTERIDX aicidx_instInClusterJ, <a class="el" href="classmat_1_1_matrix_triang.html">mat::MatrixTriang</a>&lt; T_METRIC &gt; &amp;aimatrixtriagt_dissimilarity, <a class="el" href="classds_1_1_partition_linked.html">ds::PartitionLinked</a>&lt; T_CLUSTERIDX &gt; &amp;aipartlink_memberShip, const std::vector&lt; T_INSTANCES_CLUSTER_K &gt; &amp;aivectorit_numInstClusterK)</td></tr>
<tr class="memdesc:a0be96553f39d25c65bfea9c45f05eaae"><td class="mdescLeft">&#160;</td><td class="mdescRight">Silhouette <a class="el" href="citelist.html#CITEREF_Kaufman:Rousseeuw:Book:ClusterAnalysis:1990">[25]</a>.  <a href="#a0be96553f39d25c65bfea9c45f05eaae">More...</a><br /></td></tr>
<tr class="separator:a0be96553f39d25c65bfea9c45f05eaae"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1fa2ec9d0840e8dbfa3d2737a5615b11"><td class="memTemplParams" colspan="2">template&lt;typename T_FEATURE , typename INPUT_ITERATOR , typename T_CLUSTERIDX , typename T_INSTANCES_CLUSTER_K , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a1fa2ec9d0840e8dbfa3d2737a5615b11"><td class="memTemplItemLeft" align="right" valign="top">std::vector&lt; T_METRIC &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a1fa2ec9d0840e8dbfa3d2737a5615b11">simplifiedSilhouette</a> (const <a class="el" href="classmat_1_1_matrix_base.html">mat::MatrixBase</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clusters, const std::vector&lt; T_INSTANCES_CLUSTER_K &gt; &amp;aivectorit_numInstClusterK, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:a1fa2ec9d0840e8dbfa3d2737a5615b11"><td class="mdescLeft">&#160;</td><td class="mdescRight">Simplified Silhouette <a class="el" href="citelist.html#CITEREF_Alves:etal:GAclusteringLabelKVar:FEAC:2006">[2]</a>.  <a href="#a1fa2ec9d0840e8dbfa3d2737a5615b11">More...</a><br /></td></tr>
<tr class="separator:a1fa2ec9d0840e8dbfa3d2737a5615b11"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aabc6ca77bf38202926542ef55d03df90"><td class="memTemplParams" colspan="2">template&lt;typename T_FEATURE , typename T_METRIC &gt; </td></tr>
<tr class="memitem:aabc6ca77bf38202926542ef55d03df90"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#aabc6ca77bf38202926542ef55d03df90">dbindex</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, const std::vector&lt; T_METRIC &gt; &amp;aivectort_scatter, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:aabc6ca77bf38202926542ef55d03df90"><td class="mdescLeft">&#160;</td><td class="mdescRight">DB Index <a class="el" href="citelist.html#CITEREF_Davies:Bouldin:Metricclustering:DB:1979">[14]</a> <a class="el" href="citelist.html#CITEREF_Bandyopadhyay:Maulik:GACVarK:GCUK:2002">[5]</a>.  <a href="#aabc6ca77bf38202926542ef55d03df90">More...</a><br /></td></tr>
<tr class="separator:aabc6ca77bf38202926542ef55d03df90"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ace048a1a9c9f0a5e7b8fc4f7e57f5625"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </td></tr>
<tr class="memitem:ace048a1a9c9f0a5e7b8fc4f7e57f5625"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#ace048a1a9c9f0a5e7b8fc4f7e57f5625">dbindex</a> (const <a class="el" href="classmat_1_1_matrix_base.html">mat::MatrixBase</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clusters, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:ace048a1a9c9f0a5e7b8fc4f7e57f5625"><td class="mdescLeft">&#160;</td><td class="mdescRight">DB Index <a class="el" href="citelist.html#CITEREF_Davies:Bouldin:Metricclustering:DB:1979">[14]</a> <a class="el" href="citelist.html#CITEREF_Bandyopadhyay:Maulik:GACVarK:GCUK:2002">[5]</a>.  <a href="#ace048a1a9c9f0a5e7b8fc4f7e57f5625">More...</a><br /></td></tr>
<tr class="separator:ace048a1a9c9f0a5e7b8fc4f7e57f5625"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aed03e1346938eb895882fb6ff22308c8"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_METRIC , typename T_FEATURE &gt; </td></tr>
<tr class="memitem:aed03e1346938eb895882fb6ff22308c8"><td class="memTemplItemLeft" align="right" valign="top">std::pair&lt; T_METRIC, bool &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#aed03e1346938eb895882fb6ff22308c8">SSE</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:aed03e1346938eb895882fb6ff22308c8"><td class="mdescLeft">&#160;</td><td class="mdescRight">SSE <a class="el" href="citelist.html#CITEREF_Bandyopadhyay:Maulik:GAclustering:KGA:2002">[4]</a> <a class="el" href="citelist.html#CITEREF_Chang:etal:GAclustering:GAGR:2009">[11]</a>. A boolean is also returned to indicate if the partition is valid.  <a href="#aed03e1346938eb895882fb6ff22308c8">More...</a><br /></td></tr>
<tr class="separator:aed03e1346938eb895882fb6ff22308c8"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a5939dcdd8d3b63e8b68461d6a81830b2"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_METRIC , typename T_FEATURE , typename T_CLUSTERIDX &gt; </td></tr>
<tr class="memitem:a5939dcdd8d3b63e8b68461d6a81830b2"><td class="memTemplItemLeft" align="right" valign="top">std::pair&lt; T_METRIC, bool &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a5939dcdd8d3b63e8b68461d6a81830b2">SSE</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clusters, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:a5939dcdd8d3b63e8b68461d6a81830b2"><td class="mdescLeft">&#160;</td><td class="mdescRight">SSE <a class="el" href="citelist.html#CITEREF_Bandyopadhyay:Maulik:GAclustering:KGA:2002">[4]</a> <a class="el" href="citelist.html#CITEREF_Chang:etal:GAclustering:GAGR:2009">[11]</a>. A boolean is also returned to indicate if the partition is valid.  <a href="#a5939dcdd8d3b63e8b68461d6a81830b2">More...</a><br /></td></tr>
<tr class="separator:a5939dcdd8d3b63e8b68461d6a81830b2"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af40d060af41e7e24220a41d8886e543a"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_CLUSTERIDX , typename T_FEATURE , typename T_METRIC &gt; </td></tr>
<tr class="memitem:af40d060af41e7e24220a41d8886e543a"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#af40d060af41e7e24220a41d8886e543a">SSE</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, T_CLUSTERIDX *aiarraycidx_memberShip, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:af40d060af41e7e24220a41d8886e543a"><td class="mdescLeft">&#160;</td><td class="mdescRight">SSE <a class="el" href="citelist.html#CITEREF_Bandyopadhyay:Maulik:GAclustering:KGA:2002">[4]</a> <a class="el" href="citelist.html#CITEREF_Chang:etal:GAclustering:GAGR:2009">[11]</a>. Also known as Total within cluster variation (TWCV) <a class="el" href="citelist.html#CITEREF_Murthy:Chowdhury:GAclustering:GA:1996">[35]</a> <a class="el" href="citelist.html#CITEREF_Lu:etal:GAclusteringLabel:FGKA:2004">[28]</a>.  <a href="#af40d060af41e7e24220a41d8886e543a">More...</a><br /></td></tr>
<tr class="separator:af40d060af41e7e24220a41d8886e543a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4fe497f33b0e77e7979f2de3ec4c35e3"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename FUNCINSTFREQUENCY , typename T_METRIC &gt; </td></tr>
<tr class="memitem:a4fe497f33b0e77e7979f2de3ec4c35e3"><td class="memTemplItemLeft" align="right" valign="top">std::pair&lt; T_METRIC, bool &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a4fe497f33b0e77e7979f2de3ec4c35e3">distortion</a> (const <a class="el" href="classmat_1_1_matrix_base.html">mat::MatrixBase</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, T_CLUSTERIDX *aiarraycidx_memberShip, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist, const FUNCINSTFREQUENCY func_instfrequency)</td></tr>
<tr class="separator:a4fe497f33b0e77e7979f2de3ec4c35e3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab801066e916692e30aeb8f1c8742e25b"><td class="memTemplParams" colspan="2">template&lt;typename T_FEATURE , typename T_INSTANCES_CLUSTER_K , typename T_METRIC &gt; </td></tr>
<tr class="memitem:ab801066e916692e30aeb8f1c8742e25b"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#ab801066e916692e30aeb8f1c8742e25b">distortion</a> (T_FEATURE *aiarrayt_centroid1, T_INSTANCES_CLUSTER_K aiit_numInstClusterK1, T_FEATURE *aiarrayt_centroid2, T_INSTANCES_CLUSTER_K aiit_numInstClusterK2, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="memdesc:ab801066e916692e30aeb8f1c8742e25b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Distortion metric distance between two centroids <a class="el" href="citelist.html#CITEREF_Franti:etal:GAclustering:gafranti:1997">[17]</a>.  <a href="#ab801066e916692e30aeb8f1c8742e25b">More...</a><br /></td></tr>
<tr class="separator:ab801066e916692e30aeb8f1c8742e25b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae9a204f8668a92063c9d5446a3ca9186"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_METRIC , typename T_FEATURE , typename T_BITSIZE &gt; </td></tr>
<tr class="memitem:ae9a204f8668a92063c9d5446a3ca9186"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#ae9a204f8668a92063c9d5446a3ca9186">j1</a> (<a class="el" href="classmat_1_1_bit_matrix.html">mat::BitMatrix</a>&lt; T_BITSIZE &gt; &amp;aicrispmatrix_partition, <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="separator:ae9a204f8668a92063c9d5446a3ca9186"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af6c827889147fec6e2a1d0b55eac10dd"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_METRIC , typename T_FEATURE &gt; </td></tr>
<tr class="memitem:af6c827889147fec6e2a1d0b55eac10dd"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#af6c827889147fec6e2a1d0b55eac10dd">jm</a> (<a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_METRIC &gt; &amp;aimatrixt_u, <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, T_METRIC aif_m, <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="separator:af6c827889147fec6e2a1d0b55eac10dd"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad23c0567fb4c517ab9eaa0134af14bb5"><td class="memTemplParams" colspan="2">template&lt;typename T_METRIC , typename T_CLUSTERIDX &gt; </td></tr>
<tr class="memitem:ad23c0567fb4c517ab9eaa0134af14bb5"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#ad23c0567fb4c517ab9eaa0134af14bb5">SSEMedoid</a> (const <a class="el" href="common_8hpp.html#a3f6c33fb604556cdc425e7aa2289d009">uintidx</a> *aiarrayidxinst_medoids, const T_CLUSTERIDX aicidx_numClustersK, const <a class="el" href="classmat_1_1_matrix_triang.html">mat::MatrixTriang</a>&lt; T_METRIC &gt; &amp;aimatrixtriagt_dissimilarity)</td></tr>
<tr class="memdesc:ad23c0567fb4c517ab9eaa0134af14bb5"><td class="mdescLeft">&#160;</td><td class="mdescRight">SSEMedoid <a class="el" href="citelist.html#CITEREF_Lucasius:etal:GAclusteringMedoid:GCA:1993">[30]</a>.  <a href="#ad23c0567fb4c517ab9eaa0134af14bb5">More...</a><br /></td></tr>
<tr class="separator:ad23c0567fb4c517ab9eaa0134af14bb5"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aadd2b2ab931040fc9f03f87e5f3bfc42"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_METRIC , typename T_FEATURE &gt; </td></tr>
<tr class="memitem:aadd2b2ab931040fc9f03f87e5f3bfc42"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#aadd2b2ab931040fc9f03f87e5f3bfc42">indexI</a> (<a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_METRIC &gt; &amp;aimatrixt_u, <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist, const T_METRIC airt_p=2.0)</td></tr>
<tr class="memdesc:aadd2b2ab931040fc9f03f87e5f3bfc42"><td class="mdescLeft">&#160;</td><td class="mdescRight">Validity index I or index I for a fuzzy c-partition <a class="el" href="citelist.html#CITEREF_Maulik:Bandyopadhyay:GAclustering:IndexI:2002">[33]</a> <a class="el" href="citelist.html#CITEREF_Bandyopadhuay:Maulik:GAclustering:MO:2007">[3]</a>.  <a href="#aadd2b2ab931040fc9f03f87e5f3bfc42">More...</a><br /></td></tr>
<tr class="separator:aadd2b2ab931040fc9f03f87e5f3bfc42"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:afa50845f07bcd5c00518d77d2d6a702c"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </td></tr>
<tr class="memitem:afa50845f07bcd5c00518d77d2d6a702c"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#afa50845f07bcd5c00518d77d2d6a702c">indexI</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clusters, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist, const T_METRIC airt_p=2.0)</td></tr>
<tr class="memdesc:afa50845f07bcd5c00518d77d2d6a702c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Validity index I for a crisp partition <a class="el" href="citelist.html#CITEREF_Maulik:Bandyopadhyay:GAclustering:IndexI:2002">[33]</a> <a class="el" href="citelist.html#CITEREF_Bandyopadhuay:Maulik:GAclustering:MO:2007">[3]</a>.  <a href="#afa50845f07bcd5c00518d77d2d6a702c">More...</a><br /></td></tr>
<tr class="separator:afa50845f07bcd5c00518d77d2d6a702c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a719ad18e4241520afe7b03b7fdaf84cc"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_METRIC , typename T_FEATURE &gt; </td></tr>
<tr class="memitem:a719ad18e4241520afe7b03b7fdaf84cc"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a719ad18e4241520afe7b03b7fdaf84cc">indexIreeval</a> (<a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_METRIC &gt; &amp;aimatrixt_u, <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist, const T_METRIC airt_p=2.0)</td></tr>
<tr class="memdesc:a719ad18e4241520afe7b03b7fdaf84cc"><td class="mdescLeft">&#160;</td><td class="mdescRight">Validity index I or index I for a fuzzy c-partition <a class="el" href="citelist.html#CITEREF_Maulik:Bandyopadhyay:GAclustering:IndexI:2002">[33]</a> <a class="el" href="citelist.html#CITEREF_Bandyopadhuay:Maulik:GAclustering:MO:2007">[3]</a>. Use this function when the data set changes in the same execution, parameter <img class="formulaInl" alt="$E_1$" src="form_114.png"/> is recalculated.  <a href="#a719ad18e4241520afe7b03b7fdaf84cc">More...</a><br /></td></tr>
<tr class="separator:a719ad18e4241520afe7b03b7fdaf84cc"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af7a7618cacdf1945856e037488f7a91a"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </td></tr>
<tr class="memitem:af7a7618cacdf1945856e037488f7a91a"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#af7a7618cacdf1945856e037488f7a91a">indexIreeval</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clusters, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist, const T_METRIC airt_p=2.0)</td></tr>
<tr class="memdesc:af7a7618cacdf1945856e037488f7a91a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Validity index I for a crisp partition <a class="el" href="citelist.html#CITEREF_Maulik:Bandyopadhyay:GAclustering:IndexI:2002">[33]</a> <a class="el" href="citelist.html#CITEREF_Bandyopadhuay:Maulik:GAclustering:MO:2007">[3]</a>. Use this function when the data set changes in the same execution, parameter <img class="formulaInl" alt="$E_1$" src="form_114.png"/> is recalculated.  <a href="#af7a7618cacdf1945856e037488f7a91a">More...</a><br /></td></tr>
<tr class="separator:af7a7618cacdf1945856e037488f7a91a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a14c1794b4859283fc63f3f804c5c3e72"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_METRIC , typename T_FEATURE &gt; </td></tr>
<tr class="memitem:a14c1794b4859283fc63f3f804c5c3e72"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a14c1794b4859283fc63f3f804c5c3e72">xb</a> (<a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_METRIC &gt; &amp;aimatrixt_u, <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="separator:a14c1794b4859283fc63f3f804c5c3e72"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af99b31fe06567c23441976e67cea1651"><td class="memTemplParams" colspan="2">template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </td></tr>
<tr class="memitem:af99b31fe06567c23441976e67cea1651"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#af99b31fe06567c23441976e67cea1651">xb</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;aimatrixt_centroids, INPUT_ITERATOR aiiterator_instfirst, const INPUT_ITERATOR aiiterator_instlast, <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;aipartition_clusters, const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;aifunc2p_dist)</td></tr>
<tr class="separator:af99b31fe06567c23441976e67cea1651"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a184b50b24f3a042931e256c750ba4d8e"><td class="memTemplParams" colspan="2">template&lt;typename T_METRIC &gt; </td></tr>
<tr class="memitem:a184b50b24f3a042931e256c750ba4d8e"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a184b50b24f3a042931e256c750ba4d8e">entropy</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_METRIC &gt; &amp;aimatrixt_u)</td></tr>
<tr class="memdesc:a184b50b24f3a042931e256c750ba4d8e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get entropy <img class="formulaInl" alt="$ H_c(U) $" src="form_119.png"/> <a class="el" href="citelist.html#CITEREF_Bezdek:etal:ClusterAnalysis:FCM:1984">[6]</a>.  <a href="#a184b50b24f3a042931e256c750ba4d8e">More...</a><br /></td></tr>
<tr class="separator:a184b50b24f3a042931e256c750ba4d8e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1a75de59a8b3b5ba1080b6e6c0f3c18b"><td class="memTemplParams" colspan="2">template&lt;typename T_METRIC &gt; </td></tr>
<tr class="memitem:a1a75de59a8b3b5ba1080b6e6c0f3c18b"><td class="memTemplItemLeft" align="right" valign="top">T_METRIC&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceum.html#a1a75de59a8b3b5ba1080b6e6c0f3c18b">partitioncoefficient</a> (const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_METRIC &gt; &amp;aimatrixt_u)</td></tr>
<tr class="memdesc:a1a75de59a8b3b5ba1080b6e6c0f3c18b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get partition coefficient <img class="formulaInl" alt="$ F_c(U) $" src="form_121.png"/> <a class="el" href="citelist.html#CITEREF_Bezdek:etal:ClusterAnalysis:FCM:1984">[6]</a>.  <a href="#a1a75de59a8b3b5ba1080b6e6c0f3c18b">More...</a><br /></td></tr>
<tr class="separator:a1a75de59a8b3b5ba1080b6e6c0f3c18b"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Unsupervised measures for clustering analysis. </p>
<p>Evaluate tries to determine the quality of a given obtained partition of the data without any external information available.</p>
<dl class="section version"><dt>Version</dt><dd>1.0 </dd></dl>
<dl class="section date"><dt>Date</dt><dd>2015-2017 </dd></dl>
<dl class="section copyright"><dt>Copyright</dt><dd>GPLv3 license </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a92550dabf7b2bbc875e88e4b41850531"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a92550dabf7b2bbc875e88e4b41850531">&#9670;&nbsp;</a></span>avgRadiusClusterK()</h2>

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<div class="memtemplate">
template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </div>
      <table class="memname">
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          <td class="memname">std::vector&lt;T_METRIC&gt; um::avgRadiusClusterK </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_base.html">mat::MatrixBase</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clusters</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l00361">361</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="classpartition_1_1_partition.html#acb8de7c890e05872858fb7a7aa53b657">partition::Partition&lt; T_CLUSTERIDX &gt;::begin()</a>, <a class="el" href="container__out_8hpp_source.html#l00050">inout::containerprint()</a>, <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="classmat_1_1_matrix_base.html#ae3b1c4b8e9cb7e7685d7bc129f875dcd">mat::MatrixBase&lt; T_FEATURE &gt;::getRow()</a>, and <a class="el" href="classpartition_1_1_partition.html#a96660ce61740ab0287189b21833eccdf">partition::Partition&lt; T_CLUSTERIDX &gt;::next()</a>.</p>

<p class="reference">Referenced by <a class="el" href="clustering__vksubclusterbinary_8hpp_source.html#l00937">eac::clustering_vksubclusterbinary()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l03392">dbindex()</a>, and <a class="el" href="gga__vklabel_8hpp_source.html#l00073">eac::gga_vklabel()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a46870f8491e49e0e08ceb0e2f5434bb1">&#9670;&nbsp;</a></span>CSmeasure()</h2>

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<div class="memproto">
<div class="memtemplate">
template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_INSTANCES_CLUSTER_K , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC T_METRIC um::CSmeasure </td>
          <td>(</td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="classds_1_1_partition_linked_num_inst.html">ds::PartitionLinkedNumInst</a>&lt; T_CLUSTERIDX, T_INSTANCES_CLUSTER_K &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartlinknuminst_memberShip</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
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<p>CS measure <a class="el" href="citelist.html#CITEREF_Chou:Su:Lai:ClusterMeasure:CS:2004">[12]</a> <a class="el" href="citelist.html#CITEREF_Das:Abraham:Konar:GAclusteringLabelKVar:ACDE:2008">[13]</a>. </p>
<p>CS measure is a function of the ratio of the sum of within-cluster scatter to between-cluster separation. The smallest <img class="formulaInl" alt="$CS(C)$" src="form_82.png"/> indicates a valid optimal partition.</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ CS(C) = { {1 \over k} \sum_{j=1}^{k} \left\{ {1 \over |C_j| } \sum_{x_i \in C_j} { \max \atop x_{i'} \in C_j } \left\{ D(x_j,x_{j'}) \right\} \right\} \over {1 \over k} \sum_{j=1}^{k} \left\{ { \min \atop j \in k, j \neq j'} \left\{ D(\mu_j,\mu_{j'}) \right\} \right\} } \]" src="form_83.png"/>
</p>
<p>Where <img class="formulaInl" alt="$D$" src="form_62.png"/> is a distance function.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aimatrixt_centroids</td><td>a <a class="el" href="classmat_1_1_matrix_row.html" title="Matrix store items for row.">mat::MatrixRow</a> with centroids clusters </td></tr>
    <tr><td class="paramname">aipartlinknuminst_memberShip</td><td>a clusters partition in a <a class="el" href="classds_1_1_partition_linked_num_inst.html" title="A data structure for managing an instance partition with the number of instances per cluster.">ds::PartitionLinkedNumInst</a> data structure</td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l02652">2652</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="unsupervised__measures_8hpp_source.html#l02252">diameterClusterK()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00065">measuare_undefCS</a>, and <a class="el" href="unsupervised__measures_8hpp_source.html#l00287">sumMinCjCjp()</a>.</p>

<p class="reference">Referenced by <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a659ac7560d0d7b1243dd9ef479e2f80f">&#9670;&nbsp;</a></span>D2()</h2>

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template&lt;typename T_METRIC , typename T_FEATURE , typename T_CLUSTERIDX , typename INPUT_ITERATOR &gt; </div>
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          <td class="memname">T_METRIC um::D2 </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixrowt_S</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clustersBkinCi</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clustersBi</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixrowt_Vi</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const std::vector&lt; T_METRIC &gt; &amp;&#160;</td>
          <td class="paramname"><em>aivectorr_meanRadiusBk</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l00659">659</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="container__out_8hpp_source.html#l00050">inout::containerprint()</a>, <a class="el" href="classpartition_1_1_partition.html#ae8db479b240da90b4058e35ffce182ac">partition::Partition&lt; T_CLUSTERIDX &gt;::getClusterIdx()</a>, <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, and <a class="el" href="matrix_8hpp_source.html#l00181">mat::MatrixRow&lt; T_FEATURE &gt;::getRow()</a>.</p>

<p class="reference">Referenced by <a class="el" href="clustering__vksubclusterbinary_8hpp_source.html#l00937">eac::clustering_vksubclusterbinary()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#aabc6ca77bf38202926542ef55d03df90">&#9670;&nbsp;</a></span>dbindex() <span class="overload">[1/2]</span></h2>

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<div class="memtemplate">
template&lt;typename T_FEATURE , typename T_METRIC &gt; </div>
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          <td class="memname">T_METRIC um::dbindex </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const std::vector&lt; T_METRIC &gt; &amp;&#160;</td>
          <td class="paramname"><em>aivectort_scatter</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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<p>DB Index <a class="el" href="citelist.html#CITEREF_Davies:Bouldin:Metricclustering:DB:1979">[14]</a> <a class="el" href="citelist.html#CITEREF_Bandyopadhyay:Maulik:GACVarK:GCUK:2002">[5]</a>. </p>
<p>This index is a function of the ratio of the sum of within-cluster scatter to between-cluster separation </p><dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixt_centroids</td><td>a <a class="el" href="classmat_1_1_matrix_row.html" title="Matrix store items for row.">mat::MatrixRow</a> with centroids clusters </td></tr>
    <tr><td class="paramname">aivectort_scatter</td><td>a vector whith aivectort_scatter of the clusters </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l03284">3284</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="matrix__base_8hpp_source.html#l00081">mat::MatrixBase&lt; T_FEATURE &gt;::getNumColumns()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="matrix_8hpp_source.html#l00181">mat::MatrixRow&lt; T_FEATURE &gt;::getRow()</a>, and <a class="el" href="unsupervised__measures_8hpp_source.html#l00059">measuare_undefDBindex</a>.</p>

<p class="reference">Referenced by <a class="el" href="gcuk__vkcentroid_8hpp_source.html#l00072">eac::gcuk_vkcentroid()</a>, <a class="el" href="gga__vklabel_8hpp_source.html#l00073">eac::gga_vklabel()</a>, and <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ace048a1a9c9f0a5e7b8fc4f7e57f5625">&#9670;&nbsp;</a></span>dbindex() <span class="overload">[2/2]</span></h2>

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<div class="memproto">
<div class="memtemplate">
template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::dbindex </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_base.html">mat::MatrixBase</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clusters</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>DB Index <a class="el" href="citelist.html#CITEREF_Davies:Bouldin:Metricclustering:DB:1979">[14]</a> <a class="el" href="citelist.html#CITEREF_Bandyopadhyay:Maulik:GACVarK:GCUK:2002">[5]</a>. </p>
<p>This index is a function of the ratio of the sum of within-cluster scatter to between-cluster separation </p><dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixt_centroids</td><td>a <a class="el" href="classmat_1_1_matrix_base.html" title="MatrixBase.">mat::MatrixBase</a> with centroids </td></tr>
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aiiterator_instlast</td><td>an InputIterator to the final positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aipartition_clusters</td><td>a partition of instances in clusters </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l03392">3392</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="unsupervised__measures_8hpp_source.html#l00361">avgRadiusClusterK()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00081">mat::MatrixBase&lt; T_FEATURE &gt;::getNumColumns()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="classmat_1_1_matrix_base.html#ae3b1c4b8e9cb7e7685d7bc129f875dcd">mat::MatrixBase&lt; T_FEATURE &gt;::getRow()</a>, and <a class="el" href="unsupervised__measures_8hpp_source.html#l00059">measuare_undefDBindex</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a5079e5e39be0feefeda22a8033fd28be">&#9670;&nbsp;</a></span>diameterClusterK()</h2>

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template&lt;typename INPUT_ITERATOR , typename T_CLUSTERIDX , typename T_FEATURE , typename T_METRIC &gt; </div>
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        <tr>
          <td class="memname">std::vector&lt;T_METRIC&gt; um::diameterClusterK </td>
          <td>(</td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="classds_1_1_partition_linked.html">ds::PartitionLinked</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartlink_memberShip</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l02252">2252</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="container__out_8hpp_source.html#l00050">inout::containerprint()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00554">diameterClusterKj()</a>, and <a class="el" href="partition__linked_8hpp_source.html#l00084">ds::PartitionLinked&lt; T_CLUSTERIDX &gt;::getNumPartitions()</a>.</p>

<p class="reference">Referenced by <a class="el" href="unsupervised__measures_8hpp_source.html#l02652">CSmeasure()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ac9c4b9777bb97ada898b3d1bc2621996">&#9670;&nbsp;</a></span>diameterClusterKj()</h2>

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template&lt;typename T_CLUSTERIDX , typename INPUT_ITERATOR , typename T_FEATURE , typename T_METRIC &gt; </div>
      <table class="memname">
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          <td class="memname">T_METRIC um::diameterClusterKj </td>
          <td>(</td>
          <td class="paramtype">const T_CLUSTERIDX&#160;</td>
          <td class="paramname"><em>aicidx_Clusterj</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="classds_1_1_partition_linked.html">ds::PartitionLinked</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartlink_memberShip</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l00554">554</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="partition__linked_8hpp_source.html#l00372">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::begin()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00384">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::end()</a>, <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00389">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::getValue()</a>, and <a class="el" href="partition__linked_8hpp_source.html#l00378">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::next()</a>.</p>

<p class="reference">Referenced by <a class="el" href="unsupervised__measures_8hpp_source.html#l02252">diameterClusterK()</a>, and <a class="el" href="unsupervised__measures_8hpp_source.html#l02463">DunnIndex()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ae447a0558845df2a5f208de33081c167">&#9670;&nbsp;</a></span>Dinter()</h2>

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template&lt;typename T_FEATURE , typename T_INSTANCES_CLUSTER_K , typename T_CLUSTERIDX , typename T_METRIC &gt; </div>
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          <td class="memname">T_METRIC um::Dinter </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixrowt_S</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixrowt_Vi</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const std::vector&lt; T_INSTANCES_CLUSTER_K &gt; &amp;&#160;</td>
          <td class="paramname"><em>aivectort_numInstBi</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clustersBkinCi</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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<p>Dinter <a class="el" href="citelist.html#CITEREF_Tseng:Yang:GAclusteringVarK:CLUSTERING:2001">[38]</a>. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixrowt_S</td><td>a matrix with centroid S mat::MatrixRow&lt;T_FEATURE&gt; </td></tr>
    <tr><td class="paramname">aimatrixrowt_Vi</td><td>a matrix with centroid Vi </td></tr>
    <tr><td class="paramname">aivectort_numInstBi</td><td>a vector with numero number of instances in Bi </td></tr>
    <tr><td class="paramname">aipartition_clustersBkinCi</td><td>a partition of B in the groups Ci </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l00862">862</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="classpartition_1_1_partition.html#ae8db479b240da90b4058e35ffce182ac">partition::Partition&lt; T_CLUSTERIDX &gt;::getClusterIdx()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, and <a class="el" href="matrix_8hpp_source.html#l00181">mat::MatrixRow&lt; T_FEATURE &gt;::getRow()</a>.</p>

<p class="reference">Referenced by <a class="el" href="clustering__vksubclusterbinary_8hpp_source.html#l00072">eac::clustering_genetic()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#afd59ddda70e29cf009ccb0113bf0d668">&#9670;&nbsp;</a></span>Dintra()</h2>

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template&lt;typename T_FEATURE , typename T_INSTANCES_CLUSTER_K , typename T_CLUSTERIDX , typename T_METRIC &gt; </div>
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          <td class="memname">T_METRIC um::Dintra </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixrowt_S</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixrowt_Vi</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const std::vector&lt; T_INSTANCES_CLUSTER_K &gt; &amp;&#160;</td>
          <td class="paramname"><em>aivectort_numInstBi</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clustersBkinCi</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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<p>Dintra <a class="el" href="citelist.html#CITEREF_Tseng:Yang:GAclusteringVarK:CLUSTERING:2001">[38]</a>. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixrowt_S</td><td>a matrix with centroid S mat::MatrixRow&lt;T_FEATURE&gt; </td></tr>
    <tr><td class="paramname">aimatrixrowt_Vi</td><td>a matrix with centroid Vi </td></tr>
    <tr><td class="paramname">aivectort_numInstBi</td><td>a vector with numero number of instances in Bi </td></tr>
    <tr><td class="paramname">aipartition_clustersBkinCi</td><td>a partition of B in the groups Ci </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l00778">778</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="classpartition_1_1_partition.html#ae8db479b240da90b4058e35ffce182ac">partition::Partition&lt; T_CLUSTERIDX &gt;::getClusterIdx()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, and <a class="el" href="matrix_8hpp_source.html#l00181">mat::MatrixRow&lt; T_FEATURE &gt;::getRow()</a>.</p>

<p class="reference">Referenced by <a class="el" href="clustering__vksubclusterbinary_8hpp_source.html#l00072">eac::clustering_genetic()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a00ec8c8958c649a61b3094ffe6547b10">&#9670;&nbsp;</a></span>distMinIntraClusterKj()</h2>

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<div class="memproto">
<div class="memtemplate">
template&lt;typename T_CLUSTERIDX , typename INPUT_ITERATOR , typename T_FEATURE , typename T_METRIC &gt; </div>
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          <td class="memname">T_METRIC um::distMinIntraClusterKj </td>
          <td>(</td>
          <td class="paramtype">const T_CLUSTERIDX&#160;</td>
          <td class="paramname"><em>aicidx_Clusterj</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="classds_1_1_partition_linked.html">ds::PartitionLinked</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartlink_memberShip</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
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<p>Distance min intra cluster. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aicidx_Clusterj</td><td>an integer index of the cluster </td></tr>
    <tr><td class="paramname">aipartlink_memberShip</td><td>a clusters partition in a <a class="el" href="classds_1_1_partition_linked.html" title="Data structure to define the instances that belong to a cluster consecutively.">ds::PartitionLinked</a> data structure </td></tr>
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l02196">2196</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="partition__linked_8hpp_source.html#l00372">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::begin()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00384">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::end()</a>, <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00084">ds::PartitionLinked&lt; T_CLUSTERIDX &gt;::getNumPartitions()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00389">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::getValue()</a>, and <a class="el" href="partition__linked_8hpp_source.html#l00378">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::next()</a>.</p>

<p class="reference">Referenced by <a class="el" href="unsupervised__measures_8hpp_source.html#l02463">DunnIndex()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a4fe497f33b0e77e7979f2de3ec4c35e3">&#9670;&nbsp;</a></span>distortion() <span class="overload">[1/2]</span></h2>

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<div class="memtemplate">
template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename FUNCINSTFREQUENCY , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">std::pair&lt;T_METRIC,bool&gt; um::distortion </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_base.html">mat::MatrixBase</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">T_CLUSTERIDX *&#160;</td>
          <td class="paramname"><em>aiarraycidx_memberShip</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const FUNCINSTFREQUENCY&#160;</td>
          <td class="paramname"><em>func_instfrequency</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l03821">3821</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00052">measuare_undefObjetiveFunc</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00054">measuare_undefSSE</a>, and <a class="el" href="nearestinstance__operator_8hpp_source.html#l00192">nearest::NN()</a>.</p>

<p class="reference">Referenced by <a class="el" href="cbga__fkcentroid_8hpp_source.html#l00477">eac::cbga_fkcentroid()</a>, and <a class="el" href="nearestcentroids__operator_8hpp_source.html#l00127">nearest::findTwoNearestCentroids()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ab801066e916692e30aeb8f1c8742e25b">&#9670;&nbsp;</a></span>distortion() <span class="overload">[2/2]</span></h2>

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template&lt;typename T_FEATURE , typename T_INSTANCES_CLUSTER_K , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::distortion </td>
          <td>(</td>
          <td class="paramtype">T_FEATURE *&#160;</td>
          <td class="paramname"><em>aiarrayt_centroid1</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">T_INSTANCES_CLUSTER_K&#160;</td>
          <td class="paramname"><em>aiit_numInstClusterK1</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">T_FEATURE *&#160;</td>
          <td class="paramname"><em>aiarrayt_centroid2</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">T_INSTANCES_CLUSTER_K&#160;</td>
          <td class="paramname"><em>aiit_numInstClusterK2</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Distortion metric distance between two centroids <a class="el" href="citelist.html#CITEREF_Franti:etal:GAclustering:gafranti:1997">[17]</a>. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aiarrayt_centroid1</td><td>an array with the coordinates of the centroid of the first cluster </td></tr>
    <tr><td class="paramname">aiit_numInstClusterK1</td><td>number of instances of the first group </td></tr>
    <tr><td class="paramname">aiarrayt_centroid2</td><td>an array with the coordinates of the centroid of the second cluster </td></tr>
    <tr><td class="paramname">aiit_numInstClusterK2</td><td>number of instances of the second group </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l03935">3935</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

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<h2 class="memtitle"><span class="permalink"><a href="#aa66fd9714651a71aaa33964fa0ab7012">&#9670;&nbsp;</a></span>DunnIndex() <span class="overload">[1/2]</span></h2>

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template&lt;typename T_CLUSTERIDX , typename T_METRIC &gt; </div>
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          <td class="memname">T_METRIC um::DunnIndex </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="classmat_1_1_matrix_triang.html">mat::MatrixTriang</a>&lt; T_METRIC &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixtriagt_dissimilarity</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classds_1_1_partition_linked.html">ds::PartitionLinked</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartlink_memberShip</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>The Dunn Index (DI) <a class="el" href="citelist.html#CITEREF_Dunn:ClusterMeasure:CS:1974">[15]</a> <a class="el" href="citelist.html#CITEREF_Zhang:Cao:KernelclusteringLabelKVar:2011">[39]</a>. </p>
<p>The Dunn Index determines the minimum ratio between inter-cluster distance and cluster diameter for a given partitioning. It captures the notion that, in a good clustering solution, data elements within one cluster should be much closer to each other than to elements within different clusters. It is defined as</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ DI(C) = { \min \atop j \in C} \left\{ { \min \it \atop j' \in C, j' \neq j } \left\{ { \delta(C_{j},C_{j'}) \over { \max \atop j'' \in C} \{\Delta(C_{j''})\} } \right\} \right\} \]" src="form_79.png"/>
</p>
<p>Where</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \delta(C_{j},C_{j'}) = \min \left\{ d(x_{i},x_{i''}) | x_i \in C_j, x_{i''} \in C_{j''} \right\} \]" src="form_80.png"/>
</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \Delta(C_{j}) = \max \left\{ d(x_{i},x_{i''}) | x_i , x_{i''} \in C_{j} \right\} \]" src="form_81.png"/>
</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixtriagt_dissimilarity</td><td>a matrix of distances </td></tr>
    <tr><td class="paramname">aipartlink_memberShip</td><td>a clusters partition in a <a class="el" href="classds_1_1_partition_linked.html" title="Data structure to define the instances that belong to a cluster consecutively.">ds::PartitionLinked</a> data structure </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l02337">2337</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="partition__linked_8hpp_source.html#l00372">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::begin()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00384">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::end()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00084">ds::PartitionLinked&lt; T_CLUSTERIDX &gt;::getNumPartitions()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00389">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::getValue()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00066">measuare_undefDunnIndex</a>, and <a class="el" href="partition__linked_8hpp_source.html#l00378">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::next()</a>.</p>

<p class="reference">Referenced by <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a46e5d5dc027dab5f0374eb25cd8d4168">&#9670;&nbsp;</a></span>DunnIndex() <span class="overload">[2/2]</span></h2>

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template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::DunnIndex </td>
          <td>(</td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="classds_1_1_partition_linked.html">ds::PartitionLinked</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartlink_memberShip</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>The Dunn Index (DI) <a class="el" href="citelist.html#CITEREF_Dunn:ClusterMeasure:CS:1974">[15]</a> <a class="el" href="citelist.html#CITEREF_Zhang:Cao:KernelclusteringLabelKVar:2011">[39]</a>. </p>
<p>The Dunn Index determines the minimum ratio between inter-cluster distance and cluster diameter for a given partitioning. It captures the notion that, in a good clustering solution, data elements within one cluster should be much closer to each other than to elements within different clusters. It is defined as</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ DI(C) = { \min \atop j \in C} \left\{ { \min \it \atop j' \in C, j' \neq j } \left\{ { \delta(C_{j},C_{j'}) \over { \max \atop j'' \in C} \{\Delta(C_{j''})\} } \right\} \right\} \]" src="form_79.png"/>
</p>
<p>Where</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \delta(C_{j},C_{j'}) = \min \left\{ d(x_{i},x_{i''}) | x_i \in C_j, x_{i''} \in C_{j''} \right\} \]" src="form_80.png"/>
</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \Delta(C_{j}) = \max \left\{ d(x_{i},x_{i''}) | x_i , x_{i''} \in C_{j} \right\} \]" src="form_81.png"/>
</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aipartlink_memberShip</td><td>a clusters partition in a <a class="el" href="classds_1_1_partition_linked.html" title="Data structure to define the instances that belong to a cluster consecutively.">ds::PartitionLinked</a> data structure </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l02463">2463</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="unsupervised__measures_8hpp_source.html#l00554">diameterClusterKj()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l02196">distMinIntraClusterKj()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00084">ds::PartitionLinked&lt; T_CLUSTERIDX &gt;::getNumPartitions()</a>, and <a class="el" href="unsupervised__measures_8hpp_source.html#l00066">measuare_undefDunnIndex</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a826858480b2fb93f9bd133725866b3d9">&#9670;&nbsp;</a></span>e1() <span class="overload">[1/2]</span></h2>

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template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_METRIC &gt; </div>
      <table class="memname">
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          <td class="memname">T_METRIC um::e1 </td>
          <td>(</td>
          <td class="paramtype">const T_FEATURE *&#160;</td>
          <td class="paramname"><em>aiarrayt_meanInstances</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>e1 <a class="el" href="citelist.html#CITEREF_Maulik:Bandyopadhyay:GAclustering:IndexI:2002">[33]</a> </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aiiterator_instlast</td><td>an InputIterator to the final positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aiarrayt_meanInstances</td><td>an array with the average of the attributes of the instances </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l00947">947</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, and <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>.</p>

<p class="reference">Referenced by <a class="el" href="unsupervised__measures_8hpp_source.html#l04222">indexI()</a>, and <a class="el" href="unsupervised__measures_8hpp_source.html#l04535">indexIreeval()</a>.</p>
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template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename FUNCINSTFREQUENCY , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::e1 </td>
          <td>(</td>
          <td class="paramtype">const T_FEATURE *&#160;</td>
          <td class="paramname"><em>aiarrayt_meanInstances</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const FUNCINSTFREQUENCY&#160;</td>
          <td class="paramname"><em>func_instfrequency</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>e1 <a class="el" href="citelist.html#CITEREF_Maulik:Bandyopadhyay:GAclustering:IndexI:2002">[33]</a> for frequent instances </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aiiterator_instlast</td><td>an InputIterator to the final positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aiarrayt_meanInstances</td><td>an array with the average of the attributes of the instances </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
    <tr><td class="paramname">func_instfrequency</td><td>a function that returns the frequency of the instance</td></tr>
  </table>
  </dd>
</dl>
<div class="fragment"><div class="line"><a class="code" href="datatype__instance__integer_8hpp.html#a54011d8dea2721bfe1dfbb12eb861fc8">DATATYPE_REAL</a> lmetric_e1;</div><div class="line"></div><div class="line">lmetric_e1 =</div><div class="line"><a class="code" href="namespaceum.html#a826858480b2fb93f9bd133725866b3d9">um::e1</a></div><div class="line">(larray_meanFeactures,</div><div class="line">lvectorptinst_instances.begin(),</div><div class="line">lvectorptinst_instances.end(),</div><div class="line">*pfunc2p_dist, </div><div class="line">[](<span class="keyword">const</span> <a class="code" href="classdata_1_1_instance.html">data::Instance&lt;DATATYPE_INST_CENT&gt;</a>* aiinst_iter ) -&gt; <a class="code" href="datatype__instance__integer_8hpp.html#a54011d8dea2721bfe1dfbb12eb861fc8">DATATYPE_REAL</a></div><div class="line">{</div><div class="line"><a class="code" href="classdata_1_1_instance_freq.html">data::InstanceFreq</a></div><div class="line">&lt;DATATYPE_INST_CENT,</div><div class="line"><a class="code" href="datatype__instance__integer_8hpp.html#a5394f32405650822c2ac2d7f5fe87dcb">DATATYPE_INSTANCE_FREQUENCY</a></div><div class="line">&gt;</div><div class="line">*lptinstfreq_iter =</div><div class="line">(<a class="code" href="classdata_1_1_instance_freq.html">data::InstanceFreq</a></div><div class="line">&lt;DATATYPE_INST_CENT,</div><div class="line"><a class="code" href="datatype__instance__integer_8hpp.html#a5394f32405650822c2ac2d7f5fe87dcb">DATATYPE_INSTANCE_FREQUENCY</a></div><div class="line">&gt;*)</div><div class="line">aiinst_iter;</div><div class="line"></div><div class="line"><span class="keywordflow">return</span>  (<a class="code" href="datatype__instance__integer_8hpp.html#a54011d8dea2721bfe1dfbb12eb861fc8">DATATYPE_REAL</a>) lptinstfreq_iter-&gt;getFrequency(); </div><div class="line">}</div><div class="line">);</div></div><!-- fragment --> 
<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l01041">1041</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, and <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a184b50b24f3a042931e256c750ba4d8e">&#9670;&nbsp;</a></span>entropy()</h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::entropy </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_METRIC &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_u</em></td><td>)</td>
          <td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Get entropy <img class="formulaInl" alt="$ H_c(U) $" src="form_119.png"/> <a class="el" href="citelist.html#CITEREF_Bezdek:etal:ClusterAnalysis:FCM:1984">[6]</a>. </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ H_c(U) = -\sum_{i=1}^n \sum_{j=1}^k (u_{ji} \log_a( u_{ji} )) / n. \]" src="form_120.png"/>
</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixt_u</td><td>a fuzzy c-partitions <a class="el" href="classmat_1_1_matrix_row.html" title="Matrix store items for row.">mat::MatrixRow</a> </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l04958">4958</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="matrix__base_8hpp_source.html#l00081">mat::MatrixBase&lt; T_FEATURE &gt;::getNumColumns()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00086">mat::MatrixBase&lt; T_FEATURE &gt;::getNumElems()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00070">measuare_undefEntropy</a>, and <a class="el" href="matrix_8hpp_source.html#l00119">mat::MatrixRow&lt; T_FEATURE &gt;::toArray()</a>.</p>

<p class="reference">Referenced by <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#aadd2b2ab931040fc9f03f87e5f3bfc42">&#9670;&nbsp;</a></span>indexI() <span class="overload">[1/2]</span></h2>

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<div class="memproto">
<div class="memtemplate">
template&lt;typename INPUT_ITERATOR , typename T_METRIC , typename T_FEATURE &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::indexI </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_METRIC &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_u</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const T_METRIC&#160;</td>
          <td class="paramname"><em>airt_p</em> = <code>2.0</code>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Validity index I or index I for a fuzzy c-partition <a class="el" href="citelist.html#CITEREF_Maulik:Bandyopadhyay:GAclustering:IndexI:2002">[33]</a> <a class="el" href="citelist.html#CITEREF_Bandyopadhuay:Maulik:GAclustering:MO:2007">[3]</a>. </p>
<p>The <em>validity</em> <em>index</em> <em>I</em> or simply <em>Index</em> <em>I</em>. It is used as a metric to measure clustering performance. It was proposed as a measure to indicate the (goodness) validity of the solution in the cluster. It is defined as follows:</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ I(k)=\left( {1 \over k} \cdot {E_{1} \over E_{k} } \cdot D_{k}\right)^{p}, \]" src="form_108.png"/>
</p>
<p>Where <img class="formulaInl" alt="$k$" src="form_12.png"/> is the number of clusters</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ E_{k}=\sum_{j=1}^{k}\sum_{i=1}^{n}u_{ji}\left\Vert x_{i}-\mu_{j}\right\Vert, \]" src="form_109.png"/>
</p>
<p>and</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ D_{k}=\max_{j,j'=1}^{k}\left\Vert \mu_{j'}-\mu_{j}\right\Vert \]" src="form_110.png"/>
</p>
<p><img class="formulaInl" alt="$n$" src="form_92.png"/> is the total number of objects. <img class="formulaInl" alt="$U(X)=\left[u_{kj}\right]_{k \times n}$" src="form_111.png"/> is a partition matrix of the objects and <img class="formulaInl" alt="$\mu_{j}$" src="form_100.png"/> is the centroid es el centro <img class="formulaInl" alt="$j^{th}$" src="form_112.png"/>. The value of <img class="formulaInl" alt="$k$" src="form_12.png"/> that maximizes <img class="formulaInl" alt="$I(k)$" src="form_113.png"/> is considered the correct number of clusters.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">&amp;aimatrixt_u</td><td>a fuzzy c-partitions <a class="el" href="classmat_1_1_matrix_row.html" title="Matrix store items for row.">mat::MatrixRow</a> </td></tr>
    <tr><td class="paramname">aimatrixt_centroids</td><td>a <a class="el" href="classmat_1_1_matrix_row.html" title="Matrix store items for row.">mat::MatrixRow</a> with centroids clusters </td></tr>
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aiiterator_instlast</td><td>an InputIterator to the final positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
    <tr><td class="paramname">airt_p</td><td>the power used to calculate the index, by default 2.0 </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l04222">4222</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="unsupervised__measures_8hpp_source.html#l00947">e1()</a>, <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="matrix_8hpp_source.html#l00181">mat::MatrixRow&lt; T_FEATURE &gt;::getRow()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00086">maxDistCjCjp()</a>, <a class="el" href="stats__instances_8hpp_source.html#l00055">stats::meanVector()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00055">measuare_undefIndexI</a>, <a class="el" href="interface__level1_8hpp_source.html#l00135">interfacesse::sum()</a>, and <a class="el" href="stats__instances_8hpp_source.html#l00141">stats::sumFeactures()</a>.</p>

<p class="reference">Referenced by <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#afa50845f07bcd5c00518d77d2d6a702c">&#9670;&nbsp;</a></span>indexI() <span class="overload">[2/2]</span></h2>

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template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::indexI </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clusters</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const T_METRIC&#160;</td>
          <td class="paramname"><em>airt_p</em> = <code>2.0</code>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Validity index I for a crisp partition <a class="el" href="citelist.html#CITEREF_Maulik:Bandyopadhyay:GAclustering:IndexI:2002">[33]</a> <a class="el" href="citelist.html#CITEREF_Bandyopadhuay:Maulik:GAclustering:MO:2007">[3]</a>. </p>
<p>The <em>validity</em> <em>index</em> <em>I</em> or simply <em>Index</em> <em>I</em>. It is used as a metric to measure clustering performance. It was proposed as a measure to indicate the (goodness) validity of the solution in the cluster. It is defined as follows:</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ I(k)=\left( {1 \over k} \cdot {E_{1} \over E_{k} } \cdot D_{k}\right)^{p}, \]" src="form_108.png"/>
</p>
<p>Where <img class="formulaInl" alt="$k$" src="form_12.png"/> is the number of clusters</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ E_{k}=\sum_{j=1}^{k}\sum_{i=1}^{n}u_{ji}\left\Vert x_{i}-\mu_{j}\right\Vert, \]" src="form_109.png"/>
</p>
<p>and</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ D_{k}=\max_{j,j'=1}^{k}\left\Vert \mu_{j'}-\mu_{j}\right\Vert \]" src="form_110.png"/>
</p>
<p><img class="formulaInl" alt="$n$" src="form_92.png"/> is the total number of objects. <img class="formulaInl" alt="$U(X)=\left[u_{kj}\right]_{k \times n}$" src="form_111.png"/> is a partition matrix of the objects and <img class="formulaInl" alt="$\mu_{j}$" src="form_100.png"/> is the centroid es el centro <img class="formulaInl" alt="$j^{th}$" src="form_112.png"/>. The value of <img class="formulaInl" alt="$k$" src="form_12.png"/> that maximizes <img class="formulaInl" alt="$I(k)$" src="form_113.png"/> is considered the correct number of clusters.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixt_centroids</td><td>a <a class="el" href="classmat_1_1_matrix_row.html" title="Matrix store items for row.">mat::MatrixRow</a> with centroids clusters </td></tr>
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aiiterator_instlast</td><td>an InputIterator to the final positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aipartition_clusters</td><td>a crisp partition of instances in clusters </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
    <tr><td class="paramname">airt_p</td><td>the power used to calculate the index, by default 2.0 </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l04388">4388</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="unsupervised__measures_8hpp_source.html#l00947">e1()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00086">maxDistCjCjp()</a>, <a class="el" href="stats__instances_8hpp_source.html#l00055">stats::meanVector()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00055">measuare_undefIndexI</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l03522">SSE()</a>, <a class="el" href="interface__level1_8hpp_source.html#l00135">interfacesse::sum()</a>, and <a class="el" href="stats__instances_8hpp_source.html#l00141">stats::sumFeactures()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a719ad18e4241520afe7b03b7fdaf84cc">&#9670;&nbsp;</a></span>indexIreeval() <span class="overload">[1/2]</span></h2>

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template&lt;typename INPUT_ITERATOR , typename T_METRIC , typename T_FEATURE &gt; </div>
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        <tr>
          <td class="memname">T_METRIC um::indexIreeval </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_METRIC &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_u</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const T_METRIC&#160;</td>
          <td class="paramname"><em>airt_p</em> = <code>2.0</code>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Validity index I or index I for a fuzzy c-partition <a class="el" href="citelist.html#CITEREF_Maulik:Bandyopadhyay:GAclustering:IndexI:2002">[33]</a> <a class="el" href="citelist.html#CITEREF_Bandyopadhuay:Maulik:GAclustering:MO:2007">[3]</a>. Use this function when the data set changes in the same execution, parameter <img class="formulaInl" alt="$E_1$" src="form_114.png"/> is recalculated. </p>
<p>The <em>validity</em> <em>index</em> <em>I</em> or simply <em>Index</em> <em>I</em>. It is used as a metric to measure clustering performance. It was proposed as a measure to indicate the (goodness) validity of the solution in the cluster. It is defined as follows:</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ I(k)=\left( {1 \over k} \cdot {E_{1} \over E_{k} } \cdot D_{k}\right)^{p}, \]" src="form_108.png"/>
</p>
<p>Where <img class="formulaInl" alt="$k$" src="form_12.png"/> is the number of clusters</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ E_{k}=\sum_{j=1}^{k}\sum_{i=1}^{n}u_{ji}\left\Vert x_{i}-\mu_{j}\right\Vert, \]" src="form_109.png"/>
</p>
<p>and</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ D_{k}=\max_{j,j'=1}^{k}\left\Vert \mu_{j'}-\mu_{j}\right\Vert \]" src="form_110.png"/>
</p>
<p><img class="formulaInl" alt="$n$" src="form_92.png"/> is the total number of objects. <img class="formulaInl" alt="$U(X)=\left[u_{kj}\right]_{k \times n}$" src="form_111.png"/> is a partition matrix of the objects and <img class="formulaInl" alt="$\mu_{j}$" src="form_100.png"/> is the centroid es el centro <img class="formulaInl" alt="$j^{th}$" src="form_112.png"/>. The value of <img class="formulaInl" alt="$k$" src="form_12.png"/> that maximizes <img class="formulaInl" alt="$I(k)$" src="form_113.png"/> is considered the correct number of clusters.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">&amp;aimatrixt_u</td><td>a fuzzy c-partitions <a class="el" href="classmat_1_1_matrix_row.html" title="Matrix store items for row.">mat::MatrixRow</a> </td></tr>
    <tr><td class="paramname">aimatrixt_centroids</td><td>a <a class="el" href="classmat_1_1_matrix_row.html" title="Matrix store items for row.">mat::MatrixRow</a> with centroids clusters </td></tr>
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aiiterator_instlast</td><td>an InputIterator to the final positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
    <tr><td class="paramname">airt_p</td><td>the power used to calculate the index, by default 2.0 </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l04535">4535</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="unsupervised__measures_8hpp_source.html#l00947">e1()</a>, <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="matrix_8hpp_source.html#l00181">mat::MatrixRow&lt; T_FEATURE &gt;::getRow()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00086">maxDistCjCjp()</a>, <a class="el" href="stats__instances_8hpp_source.html#l00055">stats::meanVector()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00055">measuare_undefIndexI</a>, <a class="el" href="interface__level1_8hpp_source.html#l00135">interfacesse::sum()</a>, and <a class="el" href="stats__instances_8hpp_source.html#l00141">stats::sumFeactures()</a>.</p>

<p class="reference">Referenced by <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#af7a7618cacdf1945856e037488f7a91a">&#9670;&nbsp;</a></span>indexIreeval() <span class="overload">[2/2]</span></h2>

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<div class="memproto">
<div class="memtemplate">
template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::indexIreeval </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clusters</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const T_METRIC&#160;</td>
          <td class="paramname"><em>airt_p</em> = <code>2.0</code>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Validity index I for a crisp partition <a class="el" href="citelist.html#CITEREF_Maulik:Bandyopadhyay:GAclustering:IndexI:2002">[33]</a> <a class="el" href="citelist.html#CITEREF_Bandyopadhuay:Maulik:GAclustering:MO:2007">[3]</a>. Use this function when the data set changes in the same execution, parameter <img class="formulaInl" alt="$E_1$" src="form_114.png"/> is recalculated. </p>
<p>The <em>validity</em> <em>index</em> <em>I</em> or simply <em>Index</em> <em>I</em>. It is used as a metric to measure clustering performance. It was proposed as a measure to indicate the (goodness) validity of the solution in the cluster. It is defined as follows:</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ I(k)=\left( {1 \over k} \cdot {E_{1} \over E_{k} } \cdot D_{k}\right)^{p}, \]" src="form_108.png"/>
</p>
<p>Where <img class="formulaInl" alt="$k$" src="form_12.png"/> is the number of clusters</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ E_{k}=\sum_{j=1}^{k}\sum_{i=1}^{n}u_{ji}\left\Vert x_{i}-\mu_{j}\right\Vert, \]" src="form_109.png"/>
</p>
<p>and</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ D_{k}=\max_{j,j'=1}^{k}\left\Vert \mu_{j'}-\mu_{j}\right\Vert \]" src="form_110.png"/>
</p>
<p><img class="formulaInl" alt="$n$" src="form_92.png"/> is the total number of objects. <img class="formulaInl" alt="$U(X)=\left[u_{kj}\right]_{k \times n}$" src="form_111.png"/> is a partition matrix of the objects and <img class="formulaInl" alt="$\mu_{j}$" src="form_100.png"/> is the centroid es el centro <img class="formulaInl" alt="$j^{th}$" src="form_112.png"/>. The value of <img class="formulaInl" alt="$k$" src="form_12.png"/> that maximizes <img class="formulaInl" alt="$I(k)$" src="form_113.png"/> is considered the correct number of clusters.</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixt_centroids</td><td>a <a class="el" href="classmat_1_1_matrix_row.html" title="Matrix store items for row.">mat::MatrixRow</a> with centroids clusters </td></tr>
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aiiterator_instlast</td><td>an InputIterator to the final positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aipartition_clusters</td><td>a crisp partition of instances in clusters </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
    <tr><td class="paramname">airt_p</td><td>the power used to calculate the index, by default 2.0 </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l04666">4666</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="unsupervised__measures_8hpp_source.html#l00947">e1()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00086">maxDistCjCjp()</a>, <a class="el" href="stats__instances_8hpp_source.html#l00055">stats::meanVector()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00055">measuare_undefIndexI</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l03522">SSE()</a>, <a class="el" href="interface__level1_8hpp_source.html#l00135">interfacesse::sum()</a>, and <a class="el" href="stats__instances_8hpp_source.html#l00141">stats::sumFeactures()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ae9a204f8668a92063c9d5446a3ca9186">&#9670;&nbsp;</a></span>j1()</h2>

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template&lt;typename INPUT_ITERATOR , typename T_METRIC , typename T_FEATURE , typename T_BITSIZE &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::j1 </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="classmat_1_1_bit_matrix.html">mat::BitMatrix</a>&lt; T_BITSIZE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aicrispmatrix_partition</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l04000">4000</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, and <a class="el" href="matrix_8hpp_source.html#l00181">mat::MatrixRow&lt; T_FEATURE &gt;::getRow()</a>.</p>

<p class="reference">Referenced by <a class="el" href="gaclustering__fkcrispmatrix_8hpp_source.html#l00069">eac::gaclustering_fkcrispmatrix()</a>, and <a class="el" href="gaprototypes__fkmedoid_8hpp_source.html#l00069">eac::gaprototypes_fkmedoid()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#af6c827889147fec6e2a1d0b55eac10dd">&#9670;&nbsp;</a></span>jm()</h2>

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template&lt;typename INPUT_ITERATOR , typename T_METRIC , typename T_FEATURE &gt; </div>
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          <td class="memname">T_METRIC um::jm </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_METRIC &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_u</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">T_METRIC&#160;</td>
          <td class="paramname"><em>aif_m</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l04080">4080</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, and <a class="el" href="matrix_8hpp_source.html#l00181">mat::MatrixRow&lt; T_FEATURE &gt;::getRow()</a>.</p>

<p class="reference">Referenced by <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a62470812baa18b85111f619b35a012c8">&#9670;&nbsp;</a></span>maxDistCjCjp()</h2>

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template&lt;typename T_FEATURE , typename T_METRIC &gt; </div>
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          <td class="memname">T_METRIC um::maxDistCjCjp </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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<p>Find the maximum distance beteen the centroids. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixt_centroids</td><td>a <a class="el" href="classmat_1_1_matrix_row.html" title="Matrix store items for row.">mat::MatrixRow</a> with centroids </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l00086">86</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="matrix__base_8hpp_source.html#l00081">mat::MatrixBase&lt; T_FEATURE &gt;::getNumColumns()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, and <a class="el" href="matrix_8hpp_source.html#l00181">mat::MatrixRow&lt; T_FEATURE &gt;::getRow()</a>.</p>

<p class="reference">Referenced by <a class="el" href="unsupervised__measures_8hpp_source.html#l04222">indexI()</a>, and <a class="el" href="unsupervised__measures_8hpp_source.html#l04535">indexIreeval()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a4667b7aa0e2926c0f0f94afaa4a0dcf2">&#9670;&nbsp;</a></span>maxRadiusClusterK()</h2>

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template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </div>
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          <td class="memname">std::vector&lt; T_METRIC &gt; um::maxRadiusClusterK </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clusters</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Calculates the maximum radius of a cluster for a partition. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixt_centroids</td><td>a <a class="el" href="classmat_1_1_matrix_row.html" title="Matrix store items for row.">mat::MatrixRow</a> with centroids </td></tr>
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aiiterator_instlast</td><td>an InputIterator to the final positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aipartition_clusters</td><td>a <a class="el" href="classpartition_1_1_partition.html" title="Definition of the abstract class Partition, to build a cluster of a dataset.">partition::Partition</a> of instances in clusters </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l00463">463</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="classpartition_1_1_partition.html#acb8de7c890e05872858fb7a7aa53b657">partition::Partition&lt; T_CLUSTERIDX &gt;::begin()</a>, <a class="el" href="container__out_8hpp_source.html#l00050">inout::containerprint()</a>, <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="matrix_8hpp_source.html#l00181">mat::MatrixRow&lt; T_FEATURE &gt;::getRow()</a>, and <a class="el" href="classpartition_1_1_partition.html#a96660ce61740ab0287189b21833eccdf">partition::Partition&lt; T_CLUSTERIDX &gt;::next()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a3b1be7542cfeaffb6040f73e0e3c8054">&#9670;&nbsp;</a></span>minDistCjCjp() <span class="overload">[1/2]</span></h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename T_FEATURE , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::minDistCjCjp </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l00151">151</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="matrix__base_8hpp_source.html#l00081">mat::MatrixBase&lt; T_FEATURE &gt;::getNumColumns()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, and <a class="el" href="matrix_8hpp_source.html#l00181">mat::MatrixRow&lt; T_FEATURE &gt;::getRow()</a>.</p>

<p class="reference">Referenced by <a class="el" href="clustering__vksubclusterbinary_8hpp_source.html#l00937">eac::clustering_vksubclusterbinary()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l02547">simplifiedDunnIndex()</a>, and <a class="el" href="unsupervised__measures_8hpp_source.html#l04806">xb()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ae2f7f8496b7cfe11e8411fe1102bcf22">&#9670;&nbsp;</a></span>minDistCjCjp() <span class="overload">[2/2]</span></h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename T_CLUSTERIDX , typename T_FEATURE , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::minDistCjCjp </td>
          <td>(</td>
          <td class="paramtype">const T_CLUSTERIDX&#160;</td>
          <td class="paramname"><em>aicidx_Clusterj</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_base.html">mat::MatrixBase</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l00218">218</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="matrix__base_8hpp_source.html#l00081">mat::MatrixBase&lt; T_FEATURE &gt;::getNumColumns()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, and <a class="el" href="classmat_1_1_matrix_base.html#ae3b1c4b8e9cb7e7685d7bc129f875dcd">mat::MatrixBase&lt; T_FEATURE &gt;::getRow()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a1a75de59a8b3b5ba1080b6e6c0f3c18b">&#9670;&nbsp;</a></span>partitioncoefficient()</h2>

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<div class="memproto">
<div class="memtemplate">
template&lt;typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::partitioncoefficient </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_METRIC &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_u</em></td><td>)</td>
          <td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Get partition coefficient <img class="formulaInl" alt="$ F_c(U) $" src="form_121.png"/> <a class="el" href="citelist.html#CITEREF_Bezdek:etal:ClusterAnalysis:FCM:1984">[6]</a>. </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ F_c(U) = \sum_{i=1}^n \sum_{j=1}^k (u_{ji})^2 / n. \]" src="form_122.png"/>
</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixt_u</td><td>a fuzzy c-partitions <a class="el" href="classmat_1_1_matrix_row.html" title="Matrix store items for row.">mat::MatrixRow</a> </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l04997">4997</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="matrix__base_8hpp_source.html#l00081">mat::MatrixBase&lt; T_FEATURE &gt;::getNumColumns()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00086">mat::MatrixBase&lt; T_FEATURE &gt;::getNumElems()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00071">measuare_undefPartitionCoefficient</a>, and <a class="el" href="matrix_8hpp_source.html#l00119">mat::MatrixRow&lt; T_FEATURE &gt;::toArray()</a>.</p>

<p class="reference">Referenced by <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#acbada65717c92ac0a22d2f71c61526d1">&#9670;&nbsp;</a></span>radiusClusterKj()</h2>

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<div class="memproto">
<div class="memtemplate">
template&lt;typename T_CLUSTERIDX , typename INPUT_ITERATOR , typename T_FEATURE , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::radiusClusterKj </td>
          <td>(</td>
          <td class="paramtype">const T_CLUSTERIDX&#160;</td>
          <td class="paramname"><em>aicidx_Clusterj</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const T_FEATURE *&#160;</td>
          <td class="paramname"><em>ait_centroid</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="classds_1_1_partition_linked.html">ds::PartitionLinked</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartlink_memberShip</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Radius of Clusterj. </p>
<p>Find the radius of cluster j, the maximum distance between an instance of the cluster and the centroid </p><dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aicidx_Clusterj</td><td>an integer index of the cluster </td></tr>
    <tr><td class="paramname">ait_centroid</td><td>the centroid of the Clusterj </td></tr>
    <tr><td class="paramname">aipartlink_memberShip</td><td>a clusters partition in a <a class="el" href="classds_1_1_partition_linked.html" title="Data structure to define the instances that belong to a cluster consecutively.">ds::PartitionLinked</a> data structure </td></tr>
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l00602">602</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="partition__linked_8hpp_source.html#l00372">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::begin()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00384">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::end()</a>, <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00389">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::getValue()</a>, and <a class="el" href="partition__linked_8hpp_source.html#l00378">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::next()</a>.</p>

<p class="reference">Referenced by <a class="el" href="unsupervised__measures_8hpp_source.html#l02547">simplifiedDunnIndex()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a2dbfacd88668ea38547ceb1521d758b0">&#9670;&nbsp;</a></span>scoreFunction()</h2>

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<div class="memproto">
<div class="memtemplate">
template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::scoreFunction </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clusters</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Score function ( <img class="formulaInl" alt="$SF$" src="form_75.png"/>) <a class="el" href="citelist.html#CITEREF_Sandro:Benny:IanF:ClusteringMeasure:2007">[36]</a>. </p>
<p>Score function is based on inter-cluster and intra-cluster distances. The score function is used for two purposes: i) to estimate the number of clusters and ii) to evaluate the quality of the clustering results <a class="el" href="citelist.html#CITEREF_Sandro:Benny:IanF:ClusteringMeasure:2007">[36]</a>. The higher the value of the Score function, the more suitable the number of clusters. </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ SF = 1 - \frac{1}{e^{e^{bcd-wcd}}} \]" src="form_76.png"/>
</p>
<p> Where </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ bcd = \frac{\sum_{j=1}^k \| \mu_k -M \| \cdot |C_j|}{n \cdot k}, \]" src="form_77.png"/>
</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ wcd = \sum_{j=1}^k \left( \frac{1}{ |C_j|} \sum_{x_i \in C_j} \| x_i - \mu_j \| \right) \]" src="form_78.png"/>
</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixt_centroids</td><td>a <a class="el" href="classmat_1_1_matrix_row.html" title="Matrix store items for row.">mat::MatrixRow</a> with centroids clusters </td></tr>
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aiiterator_instlast</td><td>an InputIterator to the final positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aipartition_clusters</td><td>a <a class="el" href="classpartition_1_1_partition.html" title="Definition of the abstract class Partition, to build a cluster of a dataset.">partition::Partition</a> of instances in clusters </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l01939">1939</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="stats__instances_8hpp_source.html#l00055">stats::meanVector()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00068">measuare_undefScoreFunction</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01318">ssb()</a>, <a class="el" href="interface__level1_8hpp_source.html#l00135">interfacesse::sum()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01112">sumDistInstCentInK()</a>, and <a class="el" href="stats__instances_8hpp_source.html#l00141">stats::sumFeactures()</a>.</p>

<p class="reference">Referenced by <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a31ab0871217029a7b79267bd81735914">&#9670;&nbsp;</a></span>scoreFunctionreeval()</h2>

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<div class="memproto">
<div class="memtemplate">
template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::scoreFunctionreeval </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clusters</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l02065">2065</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="stats__instances_8hpp_source.html#l00055">stats::meanVector()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00068">measuare_undefScoreFunction</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01318">ssb()</a>, <a class="el" href="interface__level1_8hpp_source.html#l00135">interfacesse::sum()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01112">sumDistInstCentInK()</a>, and <a class="el" href="stats__instances_8hpp_source.html#l00141">stats::sumFeactures()</a>.</p>

<p class="reference">Referenced by <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a5cd2a0a7fb84c32e07af00e249d880d2">&#9670;&nbsp;</a></span>silhouette() <span class="overload">[1/3]</span></h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename T_CLUSTERIDX , typename T_INSTANCES_CLUSTER_K , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::silhouette </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="classmat_1_1_matrix_triang.html">mat::MatrixTriang</a>&lt; T_METRIC &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixtriagt_dissimilarity</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classds_1_1_partition_linked_num_inst.html">ds::PartitionLinkedNumInst</a>&lt; T_CLUSTERIDX, T_INSTANCES_CLUSTER_K &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartlinknuminst_memberShip</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Silhouette <a class="el" href="citelist.html#CITEREF_Alves:etal:GAclusteringLabelKVar:FEAC:2006">[2]</a>. </p>
<p>Calculate the average of Silhouette for the <img class="formulaInl" alt="$x_i$" src="form_6.png"/> instances </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ s(x_i)=\frac{b(x_i)-a(x_i)}{\max\left\{a(x_i),b(x_i)\right\} } \]" src="form_84.png"/>
</p>
 <dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixtriagt_dissimilarity</td><td>a triangular matrix with distances between instances </td></tr>
    <tr><td class="paramname">aipartlinknuminst_memberShip</td><td>a clusters partition in a <a class="el" href="classds_1_1_partition_linked_num_inst.html" title="A data structure for managing an instance partition with the number of instances per cluster.">ds::PartitionLinkedNumInst</a> data structure</td></tr>
  </table>
  </dd>
</dl>
<dl class="section note"><dt>Note</dt><dd>Reduces the complexity of <img class="formulaInl" alt="$O(d \cdot n^2)$" src="form_85.png"/> to <img class="formulaInl" alt="$O(n^2)$" src="form_86.png"/>, for data set d large better performance </dd></dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l02739">2739</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="partition__linked_8hpp_source.html#l00372">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::begin()</a>, <a class="el" href="container__out_8hpp_source.html#l00050">inout::containerprint()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00384">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::end()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00094">ds::PartitionLinked&lt; T_CLUSTERIDX &gt;::getNumInstances()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00084">ds::PartitionLinked&lt; T_CLUSTERIDX &gt;::getNumPartitions()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00389">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::getValue()</a>, <a class="el" href="partition__linked__numinst_8hpp_source.html#l00088">ds::PartitionLinkedNumInst&lt; T_CLUSTERIDX, T_INSTANCES_CLUSTER_K &gt;::getVectorNumInstClusterK()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00060">measuare_undefSilhouette</a>, and <a class="el" href="partition__linked_8hpp_source.html#l00378">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::next()</a>.</p>

<p class="reference">Referenced by <a class="el" href="cga__vklabel_8hpp_source.html#l00067">eac::cga_vklabel()</a>, <a class="el" href="gga__vklabel_8hpp_source.html#l00073">eac::gga_vklabel()</a>, and <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#abfb804a3adf4382c6b4efe519f2ce6cb">&#9670;&nbsp;</a></span>silhouette() <span class="overload">[2/3]</span></h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename INPUT_ITERATOR , typename T_CLUSTERIDX , typename T_INSTANCES_CLUSTER_K , typename T_METRIC , typename T_FEATURE &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::silhouette </td>
          <td>(</td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classds_1_1_partition_linked_num_inst.html">ds::PartitionLinkedNumInst</a>&lt; T_CLUSTERIDX, T_INSTANCES_CLUSTER_K &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartlinknuminst_memberShip</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Silhouette <a class="el" href="citelist.html#CITEREF_Kaufman:Rousseeuw:Book:ClusterAnalysis:1990">[25]</a>. </p>
<p>Calculate the average of Silhouette for the instances </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ s(x_i)=\frac{b(x_i)-a(x_i)}{\max\left\{a(x_i),b(x_i)\right\} } \]" src="form_84.png"/>
</p>
 <dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aipartlinknuminst_memberShip</td><td>a clusters partition in a <a class="el" href="classds_1_1_partition_linked_num_inst.html" title="A data structure for managing an instance partition with the number of instances per cluster.">ds::PartitionLinkedNumInst</a> data structure </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l02880">2880</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="partition__linked_8hpp_source.html#l00372">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::begin()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00384">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::end()</a>, <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00094">ds::PartitionLinked&lt; T_CLUSTERIDX &gt;::getNumInstances()</a>, <a class="el" href="partition__linked__numinst_8hpp_source.html#l00083">ds::PartitionLinkedNumInst&lt; T_CLUSTERIDX, T_INSTANCES_CLUSTER_K &gt;::getNumInstClusterK()</a>, <a class="el" href="partition__linked__numinst_8hpp_source.html#l00101">ds::PartitionLinkedNumInst&lt; T_CLUSTERIDX, T_INSTANCES_CLUSTER_K &gt;::getNumNullCluster()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00084">ds::PartitionLinked&lt; T_CLUSTERIDX &gt;::getNumPartitions()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00389">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::getValue()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00060">measuare_undefSilhouette</a>, <a class="el" href="partition__linked_8hpp_source.html#l00378">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::next()</a>, and <a class="el" href="partition__linked__numinst_8hpp_source.html#l00183">ds::PartitionLinkedNumInst&lt; T_CLUSTERIDX, T_INSTANCES_CLUSTER_K &gt;::print()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a0be96553f39d25c65bfea9c45f05eaae">&#9670;&nbsp;</a></span>silhouette() <span class="overload">[3/3]</span></h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename T_CLUSTERIDX , typename T_INSTANCES_CLUSTER_K , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::silhouette </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="common_8hpp.html#a3f6c33fb604556cdc425e7aa2289d009">uintidx</a>&#160;</td>
          <td class="paramname"><em>aiui_idxInstance</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const T_CLUSTERIDX&#160;</td>
          <td class="paramname"><em>aicidx_instInClusterJ</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classmat_1_1_matrix_triang.html">mat::MatrixTriang</a>&lt; T_METRIC &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixtriagt_dissimilarity</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classds_1_1_partition_linked.html">ds::PartitionLinked</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartlink_memberShip</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const std::vector&lt; T_INSTANCES_CLUSTER_K &gt; &amp;&#160;</td>
          <td class="paramname"><em>aivectorit_numInstClusterK</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Silhouette <a class="el" href="citelist.html#CITEREF_Kaufman:Rousseeuw:Book:ClusterAnalysis:1990">[25]</a>. </p>
<p>Calculate Silhouette for an instance </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ s(x_i)=\frac{b(x_i)-a(x_i)}{\max\left\{a(x_i),b(x_i)\right\} } \]" src="form_84.png"/>
</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aiui_idxInstance</td><td>Instance index to calculate <img class="formulaInl" alt="$ s(x_i) $" src="form_87.png"/> </td></tr>
    <tr><td class="paramname">aicidx_instInClusterJ</td><td>Index of the cluster to which the aiui_idxInstance belongs </td></tr>
    <tr><td class="paramname">aimatrixtriagt_dissimilarity</td><td>a matrix of distances </td></tr>
    <tr><td class="paramname">aipartlink_memberShip</td><td>a clusters partition in a <a class="el" href="classds_1_1_partition_linked.html" title="Data structure to define the instances that belong to a cluster consecutively.">ds::PartitionLinked</a> data structure </td></tr>
    <tr><td class="paramname">aivectorit_numInstClusterK</td><td>a vector with the number of instances per cluster </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l03038">3038</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="partition__linked_8hpp_source.html#l00372">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::begin()</a>, <a class="el" href="container__out_8hpp_source.html#l00050">inout::containerprint()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00384">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::end()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00084">ds::PartitionLinked&lt; T_CLUSTERIDX &gt;::getNumPartitions()</a>, <a class="el" href="partition__linked_8hpp_source.html#l00389">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::getValue()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00060">measuare_undefSilhouette</a>, and <a class="el" href="partition__linked_8hpp_source.html#l00378">ds::IteratorPartitionLinked&lt; T_CLUSTERIDX &gt;::next()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#aaf89404618e7aef4f4bd8398118c70b8">&#9670;&nbsp;</a></span>simplifiedDunnIndex()</h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename T_FEATURE , typename INPUT_ITERATOR , typename T_CLUSTERIDX , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::simplifiedDunnIndex </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_base.html">mat::MatrixBase</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="classds_1_1_partition_linked.html">ds::PartitionLinked</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartlink_memberShip</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>The Simplified Dunn Index (SDI) </p>
<p>To simplify the calculations of the the Dunn Index, simplifiedDunnIndex uses the centroids to calculate the radius and decrease the computational complexity</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixt_centroids</td><td>a matrix with the centroids of the clusters </td></tr>
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aipartlink_memberShip</td><td>a a clusters partition in a <a class="el" href="classds_1_1_partition_linked.html" title="Data structure to define the instances that belong to a cluster consecutively.">ds::PartitionLinked</a> data structure </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l02547">2547</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="partition__linked_8hpp_source.html#l00084">ds::PartitionLinked&lt; T_CLUSTERIDX &gt;::getNumPartitions()</a>, <a class="el" href="classmat_1_1_matrix_base.html#ae3b1c4b8e9cb7e7685d7bc129f875dcd">mat::MatrixBase&lt; T_FEATURE &gt;::getRow()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00066">measuare_undefDunnIndex</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00151">minDistCjCjp()</a>, and <a class="el" href="unsupervised__measures_8hpp_source.html#l00602">radiusClusterKj()</a>.</p>

<p class="reference">Referenced by <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a1fa2ec9d0840e8dbfa3d2737a5615b11">&#9670;&nbsp;</a></span>simplifiedSilhouette()</h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename T_FEATURE , typename INPUT_ITERATOR , typename T_CLUSTERIDX , typename T_INSTANCES_CLUSTER_K , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">std::vector&lt; T_METRIC &gt; um::simplifiedSilhouette </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_base.html">mat::MatrixBase</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clusters</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const std::vector&lt; T_INSTANCES_CLUSTER_K &gt; &amp;&#160;</td>
          <td class="paramname"><em>aivectorit_numInstClusterK</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Simplified Silhouette <a class="el" href="citelist.html#CITEREF_Alves:etal:GAclusteringLabelKVar:FEAC:2006">[2]</a>. </p>
<p>The silhouette proposed in <a class="el" href="citelist.html#CITEREF_Kaufman:Rousseeuw:Book:ClusterAnalysis:1990">[25]</a> depends on the computation of all distances between objects, leading to a computational cost of <img class="formulaInl" alt="$O(n^2)$" src="form_86.png"/>, which is often not sufficiently efficient for real-world clustering applications (e.g. data mining, text mining, gene-expression data analysis). To circumvent this limitation, a simplified silhouette can be employed. The simplified silhouette is based on the computation of distances between objects and cluster centroids, which are the mean vectors of the clusters <a class="el" href="citelist.html#CITEREF_Hruschka:Ebecken:GAClusteringLabelKVar:CGA:2003">[19]</a>. </p><dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixt_centroids</td><td>a <a class="el" href="classmat_1_1_matrix_base.html" title="MatrixBase.">mat::MatrixBase</a> with centroids </td></tr>
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aiiterator_instlast</td><td>an InputIterator to the final positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aipartition_clusters</td><td>a partition of instances in clusters </td></tr>
    <tr><td class="paramname">aivectorit_numInstClusterK</td><td>a vector with the number of instances per cluster </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l03145">3145</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="classpartition_1_1_partition.html#acb8de7c890e05872858fb7a7aa53b657">partition::Partition&lt; T_CLUSTERIDX &gt;::begin()</a>, <a class="el" href="container__out_8hpp_source.html#l00050">inout::containerprint()</a>, <a class="el" href="interface__level1_8hpp_source.html#l00046">interfacesse::copya()</a>, <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="classmat_1_1_matrix_base.html#ae3b1c4b8e9cb7e7685d7bc129f875dcd">mat::MatrixBase&lt; T_FEATURE &gt;::getRow()</a>, and <a class="el" href="classpartition_1_1_partition.html#a96660ce61740ab0287189b21833eccdf">partition::Partition&lt; T_CLUSTERIDX &gt;::next()</a>.</p>

<p class="reference">Referenced by <a class="el" href="feac__vklabel_8hpp_source.html#l00081">eac::feca_vklabel()</a>, <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>, <a class="el" href="ga__clustering__operator_8hpp_source.html#l02191">gaclusteringop::MO1()</a>, and <a class="el" href="ga__clustering__operator_8hpp_source.html#l02589">gaclusteringop::MO2()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a3d80a7d08b3df236552d73f457543a36">&#9670;&nbsp;</a></span>ssb()</h2>

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<div class="memproto">
<div class="memtemplate">
template&lt;typename T_FEATURE , typename T_INSTANCES_CLUSTER_K , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::ssb </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const T_FEATURE *&#160;</td>
          <td class="paramname"><em>aiarrayt_meanInstances</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const std::vector&lt; T_INSTANCES_CLUSTER_K &gt; &amp;&#160;</td>
          <td class="paramname"><em>aivectort_numInstancesClusterK</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>The overall between-cluster variance ssb. </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ SS_B = \sum_{j=i}^k |C_j| \| \mu_j - M \|^2 \]" src="form_67.png"/>
</p>
<p> Where <img class="formulaInl" alt="$\mu_j$" src="form_68.png"/> is the centroid of cluster <img class="formulaInl" alt="$j$" src="form_69.png"/>, <img class="formulaInl" alt="$M$" src="form_21.png"/> is the overall mean of the instances</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixt_centroids</td><td>a <a class="el" href="classmat_1_1_matrix_row.html" title="Matrix store items for row.">mat::MatrixRow</a> with centroids </td></tr>
    <tr><td class="paramname">aiarrayt_meanInstances</td><td>an array with the mean of the attributes </td></tr>
    <tr><td class="paramname">aivectort_numInstancesClusterK</td><td>a vector with the number of instances </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l01318">1318</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="matrix__base_8hpp_source.html#l00081">mat::MatrixBase&lt; T_FEATURE &gt;::getNumColumns()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, and <a class="el" href="matrix_8hpp_source.html#l00181">mat::MatrixRow&lt; T_FEATURE &gt;::getRow()</a>.</p>

<p class="reference">Referenced by <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01939">scoreFunction()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l02065">scoreFunctionreeval()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01431">VRC()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01547">VRCreeval()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01690">WBIndex()</a>, and <a class="el" href="unsupervised__measures_8hpp_source.html#l01805">WBIndexreeval()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a68fe0b2b154800cd10afb48bb8b33eb1">&#9670;&nbsp;</a></span>ssbreeval()</h2>

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<div class="memproto">
<div class="memtemplate">
template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_INSTANCES_CLUSTER_K , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::ssbreeval </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const std::vector&lt; T_INSTANCES_CLUSTER_K &gt; &amp;&#160;</td>
          <td class="paramname"><em>aivectort_numInstancesClusterK</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l01346">1346</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="matrix__base_8hpp_source.html#l00081">mat::MatrixBase&lt; T_FEATURE &gt;::getNumColumns()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="matrix_8hpp_source.html#l00181">mat::MatrixRow&lt; T_FEATURE &gt;::getRow()</a>, <a class="el" href="stats__instances_8hpp_source.html#l00055">stats::meanVector()</a>, <a class="el" href="interface__level1_8hpp_source.html#l00135">interfacesse::sum()</a>, and <a class="el" href="stats__instances_8hpp_source.html#l00141">stats::sumFeactures()</a>.</p>

<p class="reference">Referenced by <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#aed03e1346938eb895882fb6ff22308c8">&#9670;&nbsp;</a></span>SSE() <span class="overload">[1/3]</span></h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename INPUT_ITERATOR , typename T_METRIC , typename T_FEATURE &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">std::pair&lt; T_METRIC, bool &gt; um::SSE </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>SSE <a class="el" href="citelist.html#CITEREF_Bandyopadhyay:Maulik:GAclustering:KGA:2002">[4]</a> <a class="el" href="citelist.html#CITEREF_Chang:etal:GAclustering:GAGR:2009">[11]</a>. A boolean is also returned to indicate if the partition is valid. </p>
<p>SSE A common clustering criterion or quality indicator is the sum of squared error SSE measure</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ SSE=\sum_{C_j}\sum_{x_i\in C_j}(x_i-\mu_j)^{T}(x_i-\mu_j)=\sum_{C_j}\sum_{x_i\in C_j}\Vert x_i-\mu_j\Vert^{2}. \]" src="form_88.png"/>
</p>
<p>Or with some slight variation Sum of Euclidean Distance (SED):</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ SED=\sum_{C_j}\sum_{x_i\in C_j}\Vert x_i-\mu_j\Vert \]" src="form_89.png"/>
</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixt_centroids</td><td>a <a class="el" href="classmat_1_1_matrix_row.html" title="Matrix store items for row.">mat::MatrixRow</a> with centroids clusters </td></tr>
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aiiterator_instlast</td><td>an InputIterator to the final positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances</td></tr>
  </table>
  </dd>
</dl>
<dl class="section note"><dt>Note</dt><dd>The membership of an instance to a cluster for this function is determined by the nearest object rule </dd></dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l03522">3522</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, and <a class="el" href="nearestinstance__operator_8hpp_source.html#l00192">nearest::NN()</a>.</p>

<p class="reference">Referenced by <a class="el" href="gaclustering__fklabel_8hpp_source.html#l00067">eac::gaclustering_fklabel()</a>, <a class="el" href="gas__fkcentroid_8hpp_source.html#l00070">eac::gas_fkcentroid()</a>, <a class="el" href="ga__function__objective__sse_8hpp_source.html#l00113">gafuncobj::GAFuncObjSSE&lt; T_FEATURE, T_CLUSTERIDX, T_METRIC, INPUT_ITERATOR &gt;::getObjetiveFunc()</a>, <a class="el" href="gka__fklabel_8hpp_source.html#l00067">eac::gka_fklabel()</a>, <a class="el" href="igka__fklabel_8hpp_source.html#l00080">eac::igka_fklabel()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l04388">indexI()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l04666">indexIreeval()</a>, <a class="el" href="kga__fkcentroid_8hpp_source.html#l00072">eac::kga_fkcentroid()</a>, <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>, and <a class="el" href="unsupervised__measures_8hpp_source.html#l04878">xb()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a5939dcdd8d3b63e8b68461d6a81830b2">&#9670;&nbsp;</a></span>SSE() <span class="overload">[2/3]</span></h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename INPUT_ITERATOR , typename T_METRIC , typename T_FEATURE , typename T_CLUSTERIDX &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">std::pair&lt; T_METRIC, bool &gt; um::SSE </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clusters</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>SSE <a class="el" href="citelist.html#CITEREF_Bandyopadhyay:Maulik:GAclustering:KGA:2002">[4]</a> <a class="el" href="citelist.html#CITEREF_Chang:etal:GAclustering:GAGR:2009">[11]</a>. A boolean is also returned to indicate if the partition is valid. </p>
<p>SSE A common clustering criterion or quality indicator is the sum of squared error SSE measure</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ SSE=\sum_{C_j}\sum_{x_i\in C_j}(x_i-\mu_j)^{T}(x_i-\mu_j)=\sum_{C_j}\sum_{x_i\in C_j}\Vert x_i-\mu_j\Vert^{2}. \]" src="form_88.png"/>
</p>
<p>Or with some slight variation Sum of Euclidean Distance (SED):</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ SED=\sum_{C_j}\sum_{x_i\in C_j}\Vert x_i-\mu_j\Vert \]" src="form_89.png"/>
</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixt_centroids</td><td>a <a class="el" href="classmat_1_1_matrix_row.html" title="Matrix store items for row.">mat::MatrixRow</a> with centroids clusters </td></tr>
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aiiterator_instlast</td><td>an InputIterator to the final positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aipartition_clusters</td><td>a partition of instances in clusters </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l03621">3621</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="classpartition_1_1_partition.html#acb8de7c890e05872858fb7a7aa53b657">partition::Partition&lt; T_CLUSTERIDX &gt;::begin()</a>, <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="matrix_8hpp_source.html#l00181">mat::MatrixRow&lt; T_FEATURE &gt;::getRow()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00054">measuare_undefSSE</a>, and <a class="el" href="classpartition_1_1_partition.html#a96660ce61740ab0287189b21833eccdf">partition::Partition&lt; T_CLUSTERIDX &gt;::next()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#af40d060af41e7e24220a41d8886e543a">&#9670;&nbsp;</a></span>SSE() <span class="overload">[3/3]</span></h2>

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<div class="memtemplate">
template&lt;typename INPUT_ITERATOR , typename T_CLUSTERIDX , typename T_FEATURE , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::SSE </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">T_CLUSTERIDX *&#160;</td>
          <td class="paramname"><em>aiarraycidx_memberShip</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>SSE <a class="el" href="citelist.html#CITEREF_Bandyopadhyay:Maulik:GAclustering:KGA:2002">[4]</a> <a class="el" href="citelist.html#CITEREF_Chang:etal:GAclustering:GAGR:2009">[11]</a>. Also known as Total within cluster variation (TWCV) <a class="el" href="citelist.html#CITEREF_Murthy:Chowdhury:GAclustering:GA:1996">[35]</a> <a class="el" href="citelist.html#CITEREF_Lu:etal:GAclusteringLabel:FGKA:2004">[28]</a>. </p>
<p>SSE A common clustering criterion or quality indicator is the sum of squared error SSE measure</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ SSE=\sum_{C_j}\sum_{x_i\in C_j}(x_i-\mu_j)^{T}(x_i-\mu_j)=\sum_{C_j}\sum_{x_i\in C_j}\Vert x_i-\mu_j\Vert^{2}. \]" src="form_88.png"/>
</p>
<p>Or with some slight variation Sum of Euclidean Distance (SED):</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ SED=\sum_{C_j}\sum_{x_i\in C_j}\Vert x_i-\mu_j\Vert \]" src="form_89.png"/>
</p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixt_centroids</td><td>a <a class="el" href="classmat_1_1_matrix_row.html" title="Matrix store items for row.">mat::MatrixRow</a> with centroids clusters </td></tr>
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aiiterator_instlast</td><td>an InputIterator to the final positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aiarraycidx_memberShip</td><td>an array with the labels belong to the cluster </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances</td></tr>
  </table>
  </dd>
</dl>
<dl class="section note"><dt>Note</dt><dd>The membership of an instance to a cluster for this function is determined by aiarraycidx_memberShip </dd></dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l03733">3733</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, and <a class="el" href="matrix_8hpp_source.html#l00181">mat::MatrixRow&lt; T_FEATURE &gt;::getRow()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ad23c0567fb4c517ab9eaa0134af14bb5">&#9670;&nbsp;</a></span>SSEMedoid()</h2>

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<div class="memtemplate">
template&lt;typename T_METRIC , typename T_CLUSTERIDX &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::SSEMedoid </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="common_8hpp.html#a3f6c33fb604556cdc425e7aa2289d009">uintidx</a> *&#160;</td>
          <td class="paramname"><em>aiarrayidxinst_medoids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const T_CLUSTERIDX&#160;</td>
          <td class="paramname"><em>aicidx_numClustersK</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_triang.html">mat::MatrixTriang</a>&lt; T_METRIC &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixtriagt_dissimilarity</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>SSEMedoid <a class="el" href="citelist.html#CITEREF_Lucasius:etal:GAclusteringMedoid:GCA:1993">[30]</a>. </p>
<p>The cost function sum of Euclidean distances to the most representative instance </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ SED_{medoid}=\sum_{C_j}\sum_{x_i\in C_j}\Vert x_i - m_j \Vert \]" src="form_107.png"/>
</p>
<p>where <img class="formulaInl" alt="$m_j$" src="form_8.png"/> represents the <em>medoid</em> or <em>prototype</em> of cluster <img class="formulaInl" alt="$C_j$" src="form_5.png"/></p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aiarrayidxinst_medoids</td><td>an array of indexes of more representative instances </td></tr>
    <tr><td class="paramname">aicidx_numClustersK</td><td>Number of medoids or clusters </td></tr>
    <tr><td class="paramname">aimatrixtriagt_dissimilarity</td><td>a matrix of distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l04131">4131</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="matrix__triangular_8hpp_source.html#l00128">mat::MatrixTriang&lt; T_FEATURE &gt;::getNumRows()</a>, and <a class="el" href="nearestinstance__operator_8hpp_source.html#l00325">nearest::medoidsNN()</a>.</p>

<p class="reference">Referenced by <a class="el" href="gca__fkmedoid_8hpp_source.html#l00066">eac::gca_fkmedoid()</a>, <a class="el" href="hka__fkmedoid_8hpp_source.html#l00065">eac::hka_fkmedoid()</a>, and <a class="el" href="clustering__operator__medoids_8hpp_source.html#l00389">clusteringop::updateMedoids()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#aaccb7dacc3cb2d8cd7349517387c6dfb">&#9670;&nbsp;</a></span>sumDistInstCentInK() <span class="overload">[1/2]</span></h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">std::tuple&lt; std::vector&lt; T_METRIC &gt;, std::vector&lt; <a class="el" href="common_8hpp.html#a3f6c33fb604556cdc425e7aa2289d009">uintidx</a> &gt; &gt; um::sumDistInstCentInK </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_base.html">mat::MatrixBase</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clusters</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Computes the overall between-cluster variance <img class="formulaInl" alt="$SS_B$" src="form_65.png"/> and the number of instances in each cluster. </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ SS_W = \sum_{j=1}^k \sum_{x_i \in C_j} \| x_i -\mu_j\|^2 \]" src="form_66.png"/>
</p>
 <dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixt_centroids</td><td>a <a class="el" href="classmat_1_1_matrix_base.html" title="MatrixBase.">mat::MatrixBase</a> with centroids </td></tr>
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aiiterator_instlast</td><td>an InputIterator to the final positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aipartition_clusters</td><td>a <a class="el" href="classpartition_1_1_partition.html" title="Definition of the abstract class Partition, to build a cluster of a dataset.">partition::Partition</a> of instances in clusters </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l01112">1112</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="classpartition_1_1_partition.html#acb8de7c890e05872858fb7a7aa53b657">partition::Partition&lt; T_CLUSTERIDX &gt;::begin()</a>, <a class="el" href="container__out_8hpp_source.html#l00050">inout::containerprint()</a>, <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="classmat_1_1_matrix_base.html#ae3b1c4b8e9cb7e7685d7bc129f875dcd">mat::MatrixBase&lt; T_FEATURE &gt;::getRow()</a>, and <a class="el" href="classpartition_1_1_partition.html#a96660ce61740ab0287189b21833eccdf">partition::Partition&lt; T_CLUSTERIDX &gt;::next()</a>.</p>

<p class="reference">Referenced by <a class="el" href="cbga__fkcentroid_8hpp_source.html#l00477">eac::cbga_fkcentroid()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01939">scoreFunction()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l02065">scoreFunctionreeval()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01431">VRC()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01547">VRCreeval()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01690">WBIndex()</a>, and <a class="el" href="unsupervised__measures_8hpp_source.html#l01805">WBIndexreeval()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a5d6878cc3f6d19cbe897b143e94398fa">&#9670;&nbsp;</a></span>sumDistInstCentInK() <span class="overload">[2/2]</span></h2>

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template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename FUNCINSTFREQUENCY , typename T_METRIC &gt; </div>
      <table class="memname">
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          <td class="memname">std::vector&lt; T_METRIC &gt; um::sumDistInstCentInK </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_base.html">mat::MatrixBase</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clusters</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const FUNCINSTFREQUENCY&#160;</td>
          <td class="paramname"><em>func_instfrequency</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Computes the overall between-cluster variance <img class="formulaInl" alt="$SS_B$" src="form_65.png"/> for instances for frequent instances. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixt_centroids</td><td>a <a class="el" href="classmat_1_1_matrix_base.html" title="MatrixBase.">mat::MatrixBase</a> with centroids </td></tr>
    <tr><td class="paramname">aiiterator_instfirst</td><td>an InputIterator to the initial positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aiiterator_instlast</td><td>an InputIterator to the final positions of the sequence of instances </td></tr>
    <tr><td class="paramname">aipartition_clusters</td><td>a partition of instances in clusters </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
    <tr><td class="paramname">func_instfrequency</td><td>a function that returns the frequency of an instance </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l01225">1225</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="classpartition_1_1_partition.html#acb8de7c890e05872858fb7a7aa53b657">partition::Partition&lt; T_CLUSTERIDX &gt;::begin()</a>, <a class="el" href="container__out_8hpp_source.html#l00050">inout::containerprint()</a>, <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="classmat_1_1_matrix_base.html#ae3b1c4b8e9cb7e7685d7bc129f875dcd">mat::MatrixBase&lt; T_FEATURE &gt;::getRow()</a>, and <a class="el" href="classpartition_1_1_partition.html#a96660ce61740ab0287189b21833eccdf">partition::Partition&lt; T_CLUSTERIDX &gt;::next()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a1aab06d6281016beb6769fea5032ddb9">&#9670;&nbsp;</a></span>sumMinCjCjp()</h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename T_FEATURE , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::sumMinCjCjp </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Calculate minimum sum of distances between all centroids. </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \sum_{j=1}^{k} \left\{ \begin{array}{c} min\\j \in k, j \neq j' \end{array} \left\{ D(\mu_j,\mu_{j'}) \right\}\ \right\} \]" src="form_63.png"/>
</p>
<p> where <img class="formulaInl" alt="$D$" src="form_62.png"/> is a distance function </p><dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">aimatrixt_centroids</td><td>a <a class="el" href="classmat_1_1_matrix_row.html" title="Matrix store items for row.">mat::MatrixRow</a> with centroids </td></tr>
    <tr><td class="paramname">aifunc2p_dist</td><td>an object of type <a class="el" href="structdist_1_1_dist.html" title="Generic dist.">dist::Dist</a> to calculate distances </td></tr>
  </table>
  </dd>
</dl>

<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l00287">287</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="matrix__base_8hpp_source.html#l00081">mat::MatrixBase&lt; T_FEATURE &gt;::getNumColumns()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, and <a class="el" href="matrix_8hpp_source.html#l00181">mat::MatrixRow&lt; T_FEATURE &gt;::getRow()</a>.</p>

<p class="reference">Referenced by <a class="el" href="unsupervised__measures_8hpp_source.html#l02652">CSmeasure()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a02c5655fb5595af79e18a1462114be29">&#9670;&nbsp;</a></span>VRC()</h2>

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template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::VRC </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clusters</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_squaredDist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
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<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l01431">1431</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="stats__instances_8hpp_source.html#l00055">stats::meanVector()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00064">measuare_undefVRC</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01318">ssb()</a>, <a class="el" href="interface__level1_8hpp_source.html#l00135">interfacesse::sum()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01112">sumDistInstCentInK()</a>, and <a class="el" href="stats__instances_8hpp_source.html#l00141">stats::sumFeactures()</a>.</p>

<p class="reference">Referenced by <a class="el" href="gaclustering__vktreebinary_8hpp_source.html#l00070">eac::gaclustering_vktreebinary()</a>, <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>, and <a class="el" href="tgca__vkcentroid_8hpp_source.html#l00176">eac::tgca_vkcentroid()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a6336207d868d7879d55dd09259b4fab6">&#9670;&nbsp;</a></span>VRCreeval()</h2>

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template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">T_METRIC um::VRCreeval </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clusters</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_squaredDist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
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<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l01547">1547</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="stats__instances_8hpp_source.html#l00055">stats::meanVector()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00064">measuare_undefVRC</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01318">ssb()</a>, <a class="el" href="interface__level1_8hpp_source.html#l00135">interfacesse::sum()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01112">sumDistInstCentInK()</a>, and <a class="el" href="stats__instances_8hpp_source.html#l00141">stats::sumFeactures()</a>.</p>

<p class="reference">Referenced by <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a87db67beee15dca61595892f84a94315">&#9670;&nbsp;</a></span>WBIndex()</h2>

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template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </div>
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          <td class="memname">T_METRIC um::WBIndex </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clusters</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_squaredDist</em>&#160;</td>
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        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
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<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l01690">1690</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="stats__instances_8hpp_source.html#l00055">stats::meanVector()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00073">measuare_undefWBIndex</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01318">ssb()</a>, <a class="el" href="interface__level1_8hpp_source.html#l00135">interfacesse::sum()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01112">sumDistInstCentInK()</a>, and <a class="el" href="stats__instances_8hpp_source.html#l00141">stats::sumFeactures()</a>.</p>

<p class="reference">Referenced by <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#aaa61fb14db29fe31548da280b92eb35f">&#9670;&nbsp;</a></span>WBIndexreeval()</h2>

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template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </div>
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          <td class="memname">T_METRIC um::WBIndexreeval </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clusters</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_squaredDist</em>&#160;</td>
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        <tr>
          <td></td>
          <td>)</td>
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<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l01805">1805</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="stats__instances_8hpp_source.html#l00055">stats::meanVector()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00073">measuare_undefWBIndex</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01318">ssb()</a>, <a class="el" href="interface__level1_8hpp_source.html#l00135">interfacesse::sum()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l01112">sumDistInstCentInK()</a>, and <a class="el" href="stats__instances_8hpp_source.html#l00141">stats::sumFeactures()</a>.</p>

<p class="reference">Referenced by <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a14c1794b4859283fc63f3f804c5c3e72">&#9670;&nbsp;</a></span>xb() <span class="overload">[1/2]</span></h2>

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template&lt;typename INPUT_ITERATOR , typename T_METRIC , typename T_FEATURE &gt; </div>
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          <td class="memname">T_METRIC um::xb </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_METRIC &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_u</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
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<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l04806">4806</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="instance_8hpp_source.html#l00191">data::Instance&lt; T_FEATURE &gt;::getFeatures()</a>, <a class="el" href="instance_8hpp_source.html#l00145">data::Instance&lt; T_FEATURE &gt;::getNumDimensions()</a>, <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="matrix_8hpp_source.html#l00181">mat::MatrixRow&lt; T_FEATURE &gt;::getRow()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00069">measuare_undefXieBeniIndex</a>, and <a class="el" href="unsupervised__measures_8hpp_source.html#l00151">minDistCjCjp()</a>.</p>

<p class="reference">Referenced by <a class="el" href="main__gas__clustering_8cpp_source.html#l00198">main()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#af99b31fe06567c23441976e67cea1651">&#9670;&nbsp;</a></span>xb() <span class="overload">[2/2]</span></h2>

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template&lt;typename INPUT_ITERATOR , typename T_FEATURE , typename T_CLUSTERIDX , typename T_METRIC &gt; </div>
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          <td class="memname">T_METRIC um::xb </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classmat_1_1_matrix_row.html">mat::MatrixRow</a>&lt; T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aimatrixt_centroids</em>, </td>
        </tr>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instfirst</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const INPUT_ITERATOR&#160;</td>
          <td class="paramname"><em>aiiterator_instlast</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="classpartition_1_1_partition.html">partition::Partition</a>&lt; T_CLUSTERIDX &gt; &amp;&#160;</td>
          <td class="paramname"><em>aipartition_clusters</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const <a class="el" href="structdist_1_1_dist.html">dist::Dist</a>&lt; T_METRIC, T_FEATURE &gt; &amp;&#160;</td>
          <td class="paramname"><em>aifunc2p_dist</em>&#160;</td>
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          <td></td>
          <td>)</td>
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<p class="definition">Definition at line <a class="el" href="unsupervised__measures_8hpp_source.html#l04878">4878</a> of file <a class="el" href="unsupervised__measures_8hpp_source.html">unsupervised_measures.hpp</a>.</p>

<p class="reference">References <a class="el" href="matrix__base_8hpp_source.html#l00076">mat::MatrixBase&lt; T_FEATURE &gt;::getNumRows()</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00069">measuare_undefXieBeniIndex</a>, <a class="el" href="unsupervised__measures_8hpp_source.html#l00151">minDistCjCjp()</a>, and <a class="el" href="unsupervised__measures_8hpp_source.html#l03522">SSE()</a>.</p>
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